Durable and scratch-resistant anti-reflective articles

ABSTRACT

Embodiments of durable, anti-reflective articles are described. In one or more embodiments, the article includes a substrate and an optical coating disposed on the major surface. The optical coating includes an anti-reflective coating and a scratch-resistant coating forming an anti-reflective surface. The article exhibits a maximum hardness of 12 GPa or greater, as measured on the anti-reflective surface by a Berkovich Indenter Hardness Test along an indentation depth of about 100 nm or greater. The articles of some embodiments exhibit a single side average light reflectance measured at the anti-reflective surface of about 8% or less over an optical wavelength regime in the range from about 400 nm to about 800 nm and a reference point color shift in transmittance or reflectance of less than about 2. In some embodiments, the article exhibits an angular color shift of about 5 or less at all angles from normal incidence to an incident illumination angle that is 20 degrees or greater.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority under 35 U.S.C. §119 ofU.S. Provisional Application Ser. No. 62/142,114 filed Apr. 2, 2015,U.S. Provisional Application Ser. No. 62/098,836 filed Dec. 31, 2014,U.S. Provisional Application Ser. No. 62/098,819 filed Dec. 31, 2014,U.S. Provisional Application Ser. No. 62/028,014 filed Jul. 23, 2014,U.S. Provisional Application Ser. No. 62/010,092 filed Jun. 10, 2014,and U.S. Provisional Application Ser. No. 61/991,656 filed May 12, 2014,the contents of which are relied upon and incorporated herein byreference in their entirety.

BACKGROUND

The disclosure relates to durable and scratch resistant anti-reflectivearticles and methods for making the same, and more particularly toarticles with multi-layer anti-reflective coatings exhibiting abrasionresistance, scratch resistance, low reflectivity, and colorlesstransmittance and/or reflectance.

Cover articles are often used to protect critical devices withinelectronic products, to provide a user interface for input and/ordisplay, and/or many other functions. Such products include mobiledevices, such as smart phones, mp3 players and computer tablets. Coverarticles also include architectural articles, transportation articles(e.g., articles used in automotive applications, trains, aircraft, seacraft, etc.), appliance articles, or any article that requires sometransparency, scratch-resistance, abrasion resistance or a combinationthereof. These applications often demand scratch-resistance and strongoptical performance characteristics, in terms of maximum lighttransmittance and minimum reflectance. Furthermore, some coverapplications require that the color exhibited or perceived, inreflection and/or transmission, does not change appreciably as theviewing angle is changed. In display applications, this is because, ifthe color in reflection or transmission changes with viewing angle to anappreciable degree, the user of the product will perceive a change incolor or brightness of the display, which can diminish the perceivedquality of the display. In other applications, changes in color maynegatively impact the aesthetic requirements or other functionalrequirements.

The optical performance of cover articles can be improved by usingvarious anti-reflective coatings; however known anti-reflective coatingsare susceptible to wear or abrasion. Such abrasion can compromise anyoptical performance improvements achieved by the anti-reflectivecoating. For example, optical filters are often made from multilayercoatings having differing refractive indices and made from opticallytransparent dielectric material (e.g., oxides, nitrides, and fluorides).Most of the typical oxides used for such optical filters are wideband-gap materials, which do not have the requisite mechanicalproperties, such as hardness, for use in mobile devices, architecturalarticles, transportation articles or appliance articles. Nitrides anddiamond-like coatings may exhibit high hardness values but suchmaterials do not exhibit the transmittance needed for such applications.

Abrasion damage can include reciprocating sliding contact from counterface objects (e.g., fingers). In addition, abrasion damage can generateheat, which can degrade chemical bonds in the film materials and causeflaking and other types of damage to the cover glass. Since abrasiondamage is often experienced over a longer term than the single eventsthat cause scratches, the coating materials disposed experiencingabrasion damage can also oxidize, which further degrades the durabilityof the coating.

Known anti-reflective coatings are also susceptible to scratch damageand, often, even more susceptible to scratch damage than the underlyingsubstrates on which such coatings are disposed. In some instances, asignificant portion of such scratch damage includes microductilescratches, which typically include a single groove in a material havingextended length and with depths in the range from about 100 nm to about500 nm. Microductile scratches may be accompanied by other types ofvisible damage, such as sub-surface cracking, frictive cracking,chipping and/or wear. Evidence suggests that a majority of suchscratches and other visible damage is caused by sharp contact thatoccurs in a single contact event. Once a significant scratch appears onthe cover substrate, the appearance of the article is degraded since thescratch causes an increase in light scattering, which may causesignificant reduction in brightness, clarity and contrast of images onthe display. Significant scratches can also affect the accuracy andreliability of articles including touch sensitive displays. Single eventscratch damage can be contrasted with abrasion damage. Single eventscratch damage is not caused by multiple contact events, such asreciprocating sliding contact from hard counter face objects (e.g.,sand, gravel and sandpaper), nor does it typically generate heat, whichcan degrade chemical bonds in the film materials and cause flaking andother types of damage. In addition, single event scratching typicallydoes not cause oxidization or involve the same conditions that causeabrasion damage and therefore, the solutions often utilized to preventabrasion damage may not also prevent scratches. Moreover, known scratchand abrasion damage solutions often compromise the optical properties.

Accordingly, there is a need for new cover articles, and methods fortheir manufacture, which are abrasion resistant, scratch resistant andhave improved optical performance.

SUMMARY

Embodiments of durable and scratch resistant anti-reflective articlesare described. In one or more embodiments, the article includes asubstrate and an optical coating disposed on the major surface formingan anti-reflective surface. In one or more embodiments, the opticalcoating includes an anti-reflective coating.

The article exhibits scratch resistance by exhibiting a maximum hardnessof about 12 GPa or greater, as measured by a Berkovich Indenter HardnessTest, as described herein, along an indentation depth of about 50 nm orgreater (e.g., about 100 nm or greater, from about 50 nm to about 300nm, from about 50 nm to about 400 nm, from about 50 nm to about 500 nm,from about 50 nm to about 600 nm, from about 50 nm to about 1000 nm orfrom about 50 nm to about 2000 nm), on the anti-reflective surface.

The article exhibits an abrasion resistance as measured on theanti-reflective surface after a 500-cycle abrasion using a Taber Test,as described herein. In one or more embodiments, the article exhibits anabrasion resistance (as measured on the anti-reflective surface)comprising about 1% haze or less, as measured using a hazemeter havingan aperture, wherein the aperture has a diameter of about 8 mm. In oneor more embodiments, the article exhibits an abrasion resistance (asmeasured on the anti-reflective surface) comprising an average roughnessRa, as measured by atomic force microscopy, of about 12 nm or less. Inone or more embodiments, the article exhibits an abrasion resistance (asmeasured on the anti-reflective surface) comprising a scattered lightintensity of about 0.05 (in units of 1/steradian) or less, at a polarscattering angle of about 40 degrees or less, as measured at normalincidence in transmission using an imaging sphere for scattermeasurements, with a 2 mm aperture at 600 nm wavelength. In someinstances, the article exhibits an abrasion resistance (as measured onthe anti-reflective surface) comprising a scattered light intensity ofabout 0.1 (in units of 1/steradian) or less, at a polar scattering angleof about 20 degrees or less, as measured at normal incidence intransmission using an imaging sphere for scatter measurements, with a 2mm aperture at 600 nm wavelength.

The article of one or more embodiments exhibits superior opticalperformance in terms of light transmittance and/or light reflectance. Inone or more embodiments, the article exhibits an average lighttransmittance (measured on the anti-reflective surface only) of about92% or greater (e.g., about 98% or greater) over an optical wavelengthregime (e.g., in the range from about 400 nm to about 800 nm or fromabout 450 nm to about 650 nm). In some embodiments, the article exhibitsan average light reflectance (measured at the anti-reflective surfaceonly) of about 2% or less (e.g., about 1% or less) over the opticalwavelength regime. The article may exhibits an average lighttransmittance or average light reflectance having an average oscillationamplitude of about 1 percentage points or less over the opticalwavelength regime. In one or more embodiments, the article exhibits anaverage photopic reflectance of about 1% or less at normal incidence, asmeasured on only the anti-reflective surface. In some embodiments, thearticle exhibits a single-side average photopic reflectance, measured atnormal or near-normal incidence (e.g. 0-10 degrees) on theanti-reflective surface only of less than about 10%. In someembodiments, the single-side average photopic reflectance is about 9% orless, about 8% or less, about 7% or less, about 6% or less, about 5% orless, about 4% or less, about 3%, or about 2% or less.

In some instances, the article exhibits an angular color shift (asdescribed herein) of less than about 10 (e.g., 5 or less, 4 or less, 3or less, 2 or less or about 1 or less) from a reference illuminationangle to an incident illumination angle in the range from about 2degrees to about 60 degrees, when viewed at the anti-reflective surfaceusing an illuminant. Exemplary illuminants include any one of CIE F2,CIE F10, CIE F11, CIE F12 and CIE D65. In one or more embodiment, thearticle may exhibit a b* value of less than about 2 in the CIE L*, a*,b* colorimetry system at all incidence illumination angles in the rangefrom about 0 to about 60 degrees. Alternatively or additionally, thearticle of some embodiments exhibits a transmittance color (ortransmittance color coordinates) and/or a reflectance color (orreflectance color coordinates) measured at the anti-reflective surfaceat normal incidence having a reference point color shift of less thanabout 2 from a reference point, as defined herein. In one or moreembodiments, the reference point may be the origin (0, 0) in the L*a*b*color space (or the color coordinates a*=0, b*=0 or a*=−2, b*=−2) or thetransmittance or reflectance color coordinates of the substrate. Theangular color shift, the reference point color shift and the colorcoordinates (a* and/or b*) described herein are observed under a D65and/or F2 illuminant. In some embodiments, the optical performancedescribed herein is observed under a F2 illuminant, which is known to bemore challenging due to the sharp spectral features of the F2 illuminantsource.

In one or more embodiments, the anti-reflective coating may include aplurality of layers. For example, in some embodiments, theanti-reflective coating includes a period comprising a first low RIlayer and a second high RI layer. The period may include a first low RIlayer and a second high RI disposed on the first low RI layer or viceversa. In some embodiments, the period may include a third layer. Theanti-reflective coating may include a plurality of periods such that thefirst low RI layer and the second high RI layer alternate. Theanti-reflective coating can include up to about 10 or 20 periods.

In some embodiments, the optical coating includes a scratch resistantlayer. Where scratch resistant layers are included, such layers may bedisposed on the anti-reflective coating. In other embodiments, thescratch resistant coating is disposed between the anti-reflectivecoating and the substrate. Exemplary scratch resistant layers mayexhibit a maximum hardness in the range from about 8 GPa to about 50 GPaas measured by a Berkovitch Indenter Hardness Test, as defined herein.

The scratch resistant layer may be disposed between the substrate andthe anti-reflective coating. In some embodiments, the anti-reflectivecoating may include a first portion and a second portion such that thescratch resistant layer is disposed between the first portion and thesecond portion. The thickness of the scratch-resistant layer may be inthe range from about 200 nanometers to about 3 micrometers.

In some embodiments, the article may include a layer having a refractiveindex greater than about 1.8. Materials that may be utilized in thatlayer include SiN_(x), SiO_(x)N_(y), Si_(u)Al_(v)O_(x)N_(y), AlN_(x),AlO_(x)N_(y) or a combination thereof.

In some instances, the article may include an additional layer, such asan easy-to-clean coating, a diamond-like carbon (“DLC”) coating, ascratch-resistant coating or a combination thereof. Such coatings may bedisposed on the anti-reflective coating or between layers of theanti-reflective coating.

The substrate utilized in one or more embodiments of the article caninclude an amorphous substrate or a crystalline substrate. An of anamorphous substrate includes glass that may be selected from the groupconsisting of soda lime glass, alkali aluminosilicate glass, alkalicontaining borosilicate glass and alkali aluminoborosilicate glass. Insome embodiments, the glass may be strengthened and may include acompressive stress (CS) layer with a surface CS of at least 250 MPaextending within the strengthened glass from a surface of the chemicallystrengthened glass to a depth of layer (DOL) of at least about 10 μm.

Additional features and advantages will be set forth in the detaileddescription which follows, and in part will be readily apparent to thoseskilled in the art from that description or recognized by practicing theembodiments as described herein, including the detailed descriptionwhich follows, the claims, as well as the appended drawings.

It is to be understood that both the foregoing general description andthe following detailed description are merely exemplary, and areintended to provide an overview or framework to understanding the natureand character of the claims. The accompanying drawings are included toprovide a further understanding, and are incorporated in and constitutea part of this specification. The drawings illustrate one or moreembodiment(s), and together with the description serve to explainprinciples and operation of the various embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a side view of an article, according to one or moreembodiments;

FIG. 2 is a side view of an article, according to one or more specificembodiments;

FIG. 3 is a side view of an article, according to one or moreembodiments;

FIG. 4 is a side view of an article, according to one or moreembodiments;

FIG. 5 is a side view of an article, according to one or moreembodiments;

FIG. 6 is a side view of an article, according to one or moreembodiments;

FIG. 7 is a side view of an article, according to one or moreembodiments;

FIG. 8 is a side view of an article according Example 1;

FIG. 9 is a single-sided reflectance spectra of the article of Example2, showing the reflectance as the incident illumination angle changesfrom 0° to about 60°;

FIG. 10 is a reflected color spectra of the article of Example 2 showingthe reflected color under different illuminants at different viewingangles, using a 10° observer;

FIG. 11 is a single-sided reflectance spectra of the article of Example3, showing the reflectance as the incident illumination angle changesfrom 0° to about 60°;

FIG. 12 is a reflected color spectra of the article of Example 3 showingthe reflected color under different illuminants at different viewingangles, using a 10° observer;

FIG. 13 is a reflectance spectra of Modeled Example 8, calculated fromthe anti-reflective surface only, at different viewing angles, using a10° observer;

FIG. 14 is a reflected color of the article of Example 8 showing thereflected color under different illuminants at different viewing angles,using a 10° observer;

FIG. 15 is a reflectance spectra of Modeled Example 9, calculated fromthe anti-reflective surface only, at different viewing angles, using a10° observer;

FIG. 16 is a reflected color of the article of Example 9 showing thereflected color under different illuminants at different viewing angles,using a 10° observer;

FIG. 17 is a reflectance spectra of Modeled Example 10, calculated fromthe anti-reflective surface only, at different viewing angles, using a10° observer;

FIG. 18 is a reflected color of the article of Example 10 showing thereflected color under different illuminants at different viewing angles,using a 10° observer;

FIG. 19 is a reflectance spectra of Modeled Example 11, calculated fromthe anti-reflective surface only, at different viewing angles, using a10° observer;

FIG. 20 is a reflected color of the article of Example 11 showing thereflected color under different illuminants at different viewing angles,using a 10° observer; and

FIG. 21 is a graph illustrating the hardness measurements as a functionof indentation depth and coating thickness.

DETAILED DESCRIPTION

Reference will now be made in detail to various embodiments, examples ofwhich are illustrated in the accompanying drawings.

Referring to FIG. 1, the article 100 according to one or moreembodiments may include a substrate 110, and an optical coating 120disposed on the substrate. The substrate 110 includes opposing majorsurfaces 112, 114 and opposing minor surfaces 116, 118. The opticalcoating 120 is shown in FIG. 1 as being disposed on a first opposingmajor surface 112; however, the optical coating 120 may be disposed onthe second opposing major surface 114 and/or one or both of the opposingminor surfaces, in addition to or instead of being disposed on the firstopposing major surface 112. The optical coating 120 forms ananti-reflective surface 122.

The optical coating 120 includes at least one layer of at least onematerial. The term “layer” may include a single layer or may include oneor more sub-layers. Such sub-layers may be in direct contact with oneanother. The sub-layers may be formed from the same material or two ormore different materials. In one or more alternative embodiments, suchsub-layers may have intervening layers of different materials disposedtherebetween. In one or more embodiments a layer may include one or morecontiguous and uninterrupted layers and/or one or more discontinuous andinterrupted layers (i.e., a layer having different materials formedadjacent to one another). A layer or sub-layers may be formed by anyknown method in the art, including discrete deposition or continuousdeposition processes. In one or more embodiments, the layer may beformed using only continuous deposition processes, or, alternatively,only discrete deposition processes.

The thickness of the optical coating 120 may be about 1 μm or greaterwhile still providing an article that exhibits the optical performancedescribed herein. In some examples, the optical coating 120 thicknessmay be in the range from about 1 μm to about 20 μm (e.g., from about 1μm to about 10 μm, or from about 1 μm to about 5 μm).

As used herein, the term “dispose” includes coating, depositing and/orforming a material onto a surface using any known method in the art. Thedisposed material may constitute a layer, as defined herein. The phrase“disposed on” includes the instance of forming a material onto a surfacesuch that the material is in direct contact with the surface and alsoincludes the instance where the material is formed on a surface, withone or more intervening material(s) is between the disposed material andthe surface. The intervening material(s) may constitute a layer, asdefined herein.

As shown in FIG. 2, the optical coating 120 includes an anti-reflectivecoating 130, which may include a plurality of layers (130A, 130B). Inone or more embodiments, the anti-reflective coating 130 may include aperiod 132 comprising two or more layers. In one or more embodiments,the two or more layers may be characterized as having differentrefractive indices from each another. In one embodiment, the period 132includes a first low RI layer 130A and a second high RI layer 130B. Thedifference in the refractive index of the first low RI layer and thesecond high RI layer may be about 0.01 or greater, 0.05 or greater, 0.1or greater or even 0.2 or greater.

As shown in FIG. 2, the anti-reflective coating 130 may include aplurality of periods (132). A single period includes include a first lowRI layer 130A and a second high RI layer 130B, such that when aplurality of periods are provided, the first low RI layer 130A(designated for illustration as “L”) and the second high RI layer 130B(designated for illustration as “H”) alternate in the following sequenceof layers: L/H/L/H or H/L/H/L, such that the first low RI layer and thesecond high RI layer appear to alternate along the physical thickness ofthe anti-reflective coating 120. In the example in FIG. 2, theanti-reflective coating 130 includes three periods. In some embodiments,the anti-reflective coating 130 may include up to 25 periods. Forexample, the anti-reflective coating 130 may include from about 2 toabout 20 periods, from about 2 to about 15 periods, from about 2 toabout 10 periods, from about 2 to about 12 periods, from about 3 toabout 8 periods, from about 3 to about 6 periods.

In the embodiment shown in FIG. 3, the anti-reflective coating 130 mayinclude an additional capping layer 131, which may include a lowerrefractive index material than the second high RI layer 130B. In someembodiments, the period 132 may include one or more third layers 130C,as shown in FIG. 3. The third layer(s) 130C may have a low RI, a high RIor a medium RI. In some embodiments, the third layer(s) 130C may havethe same RI as the first low RI layer 130A or the second high RI layer130B. In other embodiments, the third layer(s) 130C may have a medium RIthat is between the RI of the first low RI layer 130A and the RI of thesecond high RI layer 130B. Alternatively, the third layer(s) 130C mayhave a refractive index greater than the 2^(nd) high RI layer 130B. Thethird layer may be provided in the anti-reflective coating 120 in thefollowing exemplary configurations: L_(third layer)/H/L/H/L;H_(third layer)/L/H/L/H; L/H/L/H/L_(third layer);H/L/H/L/H_(third layer); L_(third layer)/H/L/H/L/H_(third layer);H_(third layer)/L/H/L/H/L_(third layer); L_(third layer)/L/H/L/H;H_(third layer)/H/L/H/L; H/L/H/L/L_(third layer);L/H/L/H/H_(third layer); L_(third layer)/L/H/L/H/H_(third layer);H_(third layer)/H/L/H/L/L_(third) layer; L/M_(third layer)/H/L/M/H;H/M/L/H/M/L; M/L/H/L/M; and other combinations. In these configurations,“L” without any subscript refers to the first low RI layer and “H”without any subscript refers to the second high RI layer. Reference to“L_(third sub-layer)” refers to a third layer having a low RI,“H_(third sub-layer)” refers to a third layer having a high RI and “M”refers to a third layer having a medium RI, all relative to the 1^(st)layer and the 2^(nd) layer.

As used herein, the terms “low RI”, “high RI” and “medium RI” refer tothe relative values for the RI to another (e.g., low RI<medium RI<highRI). In one or more embodiments, the term “low RI” when used with thefirst low RI layer or with the third layer, includes a range from about1.3 to about 1.7 or 1.75. In one or more embodiments, the term “high RI”when used with the second high RI layer or with the third layer,includes a range from about 1.7 to about 2.5 (e.g., about 1.85 orgreater). In some embodiments, the term “medium RI” when used with thethird layer, includes a range from about 1.55 to about 1.8. In someinstances, the ranges for low RI, high RI and medium RI may overlap;however, in most instances, the layers of the anti-reflective coating130 have the general relationship regarding RI of: low RI<medium RI<highRI.

The third layer(s) 130C may be provided as a separate layer from aperiod 132 and may be disposed between the period or plurality ofperiods and the capping layer 131, as shown in FIG. 4. The thirdlayer(s) may also be provided as a separate layer from a period 132 andmay have disposed between the substrate 110 and the plurality of periods132, as shown in FIG. 5. The third layer(s) 130C may be used in additionto an additional coating 140 instead of the capping 131 or in additionto the capping layer, as shown in FIG. 6.

Exemplary materials suitable for use in the anti-reflective coating 130include: SiO₂, Al₂O₃, GeO₂, SiO, AlOxNy, AlN, SiNx, SiO_(x)N_(y),Si_(u)Al_(v)O_(x)N_(y), Ta₂O₅, Nb₂O₅, TiO₂, ZrO₂, TiN, MgO, MgF₂, BaF₂,CaF₂, SnO₂, HfO₂, Y₂O₃, MoO₃, DyF₃, YbF₃, YF₃, CeF₃, polymers,fluoropolymers, plasma-polymerized polymers, siloxane polymers,silsesquioxanes, polyimides, fluorinated polyimides, polyetherimide,polyethersulfone, polyphenylsulfone, polycarbonate, polyethyleneterephthalate, polyethylene naphthalate, acrylic polymers, urethanepolymers, polymethylmethacrylate, other materials cited below assuitable for use in a scratch-resistant layer, and other materials knownin the art. Some examples of suitable materials for use in the first lowRI layer include SiO₂, Al₂O₃, GeO₂, SiO, AlO_(x)N_(y), SiO_(x)N_(y),Si_(u)Al_(v)O_(x)N_(y), MgO, MgAl₂O₄, MgF₂, BaF₂, CaF₂, DyF₃, YbF₃, YF₃,and CeF₃. The nitrogen content of the materials for use in the first lowRI layer may be minimized (e.g., in materials such as Al₂O₃ andMgAl₂O₄). Some examples of suitable materials for use in the second highRI layer include Si_(u)Al_(v)O_(x)N_(y), Ta₂O₅, Nb₂O₅, AlN, Si₃N₄,AlO_(x)N_(y), SiO_(x)N_(y), HfO₂, TiO₂, ZrO₂, Y₂O₃, Al₂O₃, MoO₃ anddiamond-like carbon. The oxygen content of the materials for the secondhigh RI layer and/or the scratch-resistant layer may be minimized,especially in SiNx or AlNx materials. AlO_(x)N_(y) materials may beconsidered to be oxygen-doped AlNx, that is they may have an AlNxcrystal structure (e.g. wurtzite) and need not have an AlON crystalstructure. Exemplary preferred AlO_(x)N_(y) high RI materials maycomprise from about 0 atom % to about 20 atom % oxygen, or from about 5atom % to about 15 atom % oxygen, while including 30 atom % to about 50atom % nitrogen. Exemplary preferred Si_(u)Al_(v)O_(x)N_(y) high RImaterials may comprise from about 10 atom % to about 30 atom % or fromabout 15 atom % to about 25 atom % silicon, from about 20 atom % toabout 40 atom % or from about 25 atom % to about 35 atom % aluminum,from about 0 atom % to about 20 atom % or from about 1 atom % to about20 atom % oxygen, and from about 30 atom % to about 50 atom % nitrogen.The foregoing materials may be hydrogenated up to about 30% by weight.Where a material having a medium refractive index is desired, someembodiments may utilize MN and/or SiO_(x)N_(y). The hardness of thesecond high RI layer and/or the scratch-resistant layer may becharacterized specifically. In some embodiments, the maximum hardness ofthe second high RI layer and/or the scratch-resistant layer, as measuredby the Berkovitch Indenter Hardness Test, may be about 8 GPa or greater,about 10 GPa or greater, about 12 GPa or greater, about 15 GPa orgreater, about 18 GPa or greater, or about 20 GPa or greater. In somecases, the second high RI layer material may be deposited as a singlelayer and may be characterized as a scratch resistant layer, and thissingle layer may have a thickness between about 500 and 2000 nm forrepeatable hardness determination.

In one or more embodiments at least one of the layer(s) of theanti-reflective coating 130 may include a specific optical thicknessrange. As used herein, the term “optical thickness” is determined by(n*d), where “n” refers to the RI of the sub-layer and “d” refers to thephysical thickness of the layer. In one or more embodiments, at leastone of the layers of the anti-reflective coating 130 may include anoptical thickness in the range from about 2 nm to about 200 nm, fromabout 10 nm to about 100 nm, from about 15 nm to about 100 nm, fromabout 15 to about 500 nm, or from about 15 to about 5000 nm. In someembodiments, all of the layers in the anti-reflective coating 130 mayeach have an optical thickness in the range from about 2 nm to about 200nm, from about 10 nm to about 100 nm, from about 15 nm to about 100 nm,from about 15 to about 500 nm, or from about 15 to about 5000 nm. Insome cases, at least one layer of the anti-reflective coating 130 has anoptical thickness of about 50 nm or greater. In some cases, each of thefirst low RI layers have an optical thickness in the range from about 2nm to about 200 nm, from about 10 nm to about 100 nm, from about 15 nmto about 100 nm, from about 15 to about 500 nm, or from about 15 toabout 5000 nm. In other cases, each of the second high RI layers have anoptical thickness in the range from about 2 nm to about 200 nm, fromabout 10 nm to about 100 nm, from about 15 nm to about 100 nm, fromabout 15 to about 500 nm, or from about 15 to about 5000 nm. In yetother cases, each of the third layers have an optical thickness in therange from about 2 nm to about 200 nm, from about 10 nm to about 100 nm,from about 15 nm to about 100 nm, from about 15 to about 500 nm, or fromabout 15 to about 5000 nm.

In some embodiments, the thickness of one or more of the layers of theoptical coating 130 may be minimized. In one or more embodiments, thethickness of the thickness of the high RI layer(s) and/or the medium RIlayer(s) are minimized such that they are less than about 500 nm. In oneor more embodiments, the combined thickness of the high RI layer(s), themedium RI (layers) and/or the combination of the high RI and medium RIlayers is less than about 500 nm.

In some embodiments, the amount of low RI material in the opticalcoating may be minimized Without being bound by theory, the low RImaterial is typically also a lower-hardness material, owing to thenature of atomic bonding and electron densities that simultaneouslyaffect refractive index and hardness, and thus minimizing such materialcan maximize the hardness, while maintaining the reflectance and colorperformance described herein. Expressed as a fraction of physicalthickness of the optical coating, the low RI material may comprise lessthan about 60%, less than about 50%, less than about 40%, less thanabout 30%, less than about 20%, less than about 10%, or less than about5% of the physical thickness of the optical coating. Alternately oradditionally, the amount of low RI material may be quantified as the sumof the physical thicknesses of all layer of low RI material that aredisposed above the thickest high RI layer in the optical coating (i.e.on the side opposite the substrate, user side or air side). Withoutbeing bound by theory, the thick high RI layer having a high hardnesseffectively shields the layers underneath (or between the thick RI layerand the substrate) from many or most scratches. Accordingly, the layersdisposed above the thickest high RI layer may have an outsized effect onscratch resistance of the overall article. This is especially relevantwhen the thickest high RI layer has a physical thickness that is greaterthan about 400 nm and has a hardness greater than about 12 GPa asmeasured by the Berkovich Indenter Hardness Test. The amount of low RImaterial disposed on the thickest high RI layer (i.e. on the sideopposite the substrate, user side or air side) may have a thickness lessthan or equal to about 150 nm, less than or equal to about 120 nm, lessthan or equal to about 110 nm, 100 nm, 90 nm, 80 nm, 70 nm, 60 nm, 50nm, 40 nm, 30 nm, 25 nm, 20 nm, 15 nm, or less than or equal to about 12nm.

In some embodiments, the top-most air-side layer may comprise a high RIlayer that also exhibits high hardness, as shown in Modeled Examples8-9. In some embodiments, an additional coating 140 may be disposed ontop of this top-most air-side high RI layer (e.g., the additionalcoating may include low-friction coating, an oleophobic coating, or aneasy-to-clean coating). Moreover, as illustrated by Modeled Example 10,the addition of a low RI layer having a very low thickness (e.g., about10 nm or less, about 5 nm or less or about 2 nm or less) has minimalinfluence on the optical performance, when added to the top-mostair-side layer comprising a high RI layer. The low RI layer having avery low thickness may include SiO₂, an oleophobic or low-frictionlayer, or a combination of SiO₂ and an oleophobic material. Exemplarylow-friction layers may include diamond-like carbon, such materials (orone or more layers of the optical coating) may exhibit a coefficient offriction less than 0.4, less than 0.3, less than 0.2, or even less than0.1.

In one or more embodiments, the anti-reflective coating 130 has aphysical thickness of about 800 nm or less. The anti-reflective coating130 may have a physical thickness in the range from about 10 nm to about800 nm, from about 50 nm to about 800 nm, from about 100 nm to about 800nm, from about 150 nm to about 800 nm, from about 200 nm to about 800nm, from about 10 nm to about 750 nm, from about 10 nm to about 700 nm,from about 10 nm to about 650 nm, from about 10 nm to about 600 nm, fromabout 10 nm to about 550 nm, from about 10 nm to about 500 nm, fromabout 10 nm to about 450 nm, from about 10 nm to about 400 nm, fromabout 10 nm to about 350 nm, from about 10 nm to about 300 nm, fromabout 50 to about 300, and all ranges and sub-ranges therebetween.

In one or more embodiments, the combined physical thickness of thesecond high RI layer(s) may be characterized. For example, in someembodiments, the combined thickness of the second high RI layer(s) maybe about 100 nm or greater, about 150 nm or greater, about 200 nm orgreater, about 500 nm or greater. The combined thickness is thecalculated combination of the thicknesses of the individual high RIlayer(s) in the anti-reflective coating 130, even when there areintervening low RI layer(s) or other layer(s). In some embodiments, thecombined physical thickness of the second high RI layer(s), which mayalso comprise a high-hardness material (e.g., a nitride or an oxynitridematerial), may be greater than 30% of the total physical thickness ofthe anti-reflective coating. For example, the combined physicalthickness of the second high RI layer(s) may be about 40% or greater,about 50% or greater, about 60% or greater, about 70% or greater, about75% or greater, or even about 80% or greater, of the total physicalthickness of the anti-reflective coating. Additionally or alternatively,the amount of the high refractive index material, which may also be ahigh-hardness material, included in the optical coating may becharacterized as a percentage of the physical thickness of the uppermost (i.e., user side or side of the optical coating opposite thesubstrate) 500 nm of the article or optical coating 120. Expressed as apercentage of the upper most 500 nm of the article or optical coating,the combined physical thickness of the second high RI layer(s) (or thethickness of the high refractive index material) may be about 50% orgreater, about 60% or greater, about 70% or greater, about 80% orgreater, or even about 90% or greater. In some embodiments, greaterproportions of hard and high-index material within the anti-reflectivecoating can also simultaneously be made to also exhibit low reflectance,low color, and high abrasion resistance as further described elsewhereherein. In one or more embodiments, the second high RI layers mayinclude a material having a refractive index greater than about 1.85 andthe first low RI layers may include a material having a refractive indexless than about 1.75. In some embodiments, the second high RI layers mayinclude a nitride or an oxynitride material. In some instances, thecombined thickness of all the first low RI layers in the optical coating(or in the layers that are disposed on the thickest second high RI layerof the optical coating) may be about 200 nm or less (e.g., about 150 nmor less, about 100 nm or less, about 75 nm or less, or about 50 nm orless).

In some embodiments, the anti-reflective coating 130 exhibits an averagelight reflectance of about 9% or less, about 8% or less, about 7% orless, about 6% or less, about 5% or less, about 4% or less, about 3% orless, or about 2% or less over the optical wavelength regime, whenmeasured at the anti-reflective surface 122 only (e.g., when removingthe reflections from an uncoated back surface (e.g., 114 in FIG. 1) ofthe article, such as through using index-matching oils on the backsurface coupled to an absorber, or other known methods). The averagereflectance (which may be a photopic average) may be in the range fromabout 0.4% to about 9%, from about 0.4% to about 8%, from about 0.4% toabout 7%, from about 0.4% to about 6%, or from about 0.4% to about 5%and all ranges therebetween. In some instances, the anti-reflectivecoating 120 may exhibit such average light reflectance over otherwavelength ranges such as from about 450 nm to about 650 nm, from about420 nm to about 680 nm, from about 420 nm to about 700 nm, from about420 nm to about 740 nm, from about 420 nm to about 850 nm, or from about420 nm to about 950 nm. In some embodiments, the anti-reflective surface122 exhibits an average light transmission of about 90% or greater, 92%or greater, 94% or greater, 96% or greater, or 98% or greater, over theoptical wavelength regime. Unless otherwise specified, the averagereflectance or transmittance is measured at an incident illuminationangle from about 0 degrees to about 10 degrees (however, suchmeasurements may be provided at incident illumination angles of 45degrees or 60 degrees).

The article 100 may include one or more additional coatings 140 disposedon the anti-reflective coating, as shown in FIG. 6. In one or moreembodiments, the additional coating may include an easy-to-cleancoating. An example of a suitable an easy-to-clean coating is describedin U.S. patent application Ser. No. 13/690,904, entitled “PROCESS FORMAKING OF GLASS ARTICLES WITH OPTICAL AND EASY-TO-CLEAN COATINGS,” filedon Nov. 30, 2012, which is incorporated herein in its entirety byreference. The easy-to-clean coating may have a thickness in the rangefrom about 5 nm to about 50 nm and may include known materials such asfluorinated silanes. In some embodiments, the easy-to-clean coating mayhave a thickness in the range from about 1 nm to about 40 nm, from about1 nm to about 30 nm, from about 1 nm to about 25 nm, from about 1 nm toabout 20 nm, from about 1 nm to about 15 nm, from about 1 nm to about 10nm, from about 5 nm to about 50 nm, from about 10 nm to about 50 nm,from about 15 nm to about 50 nm, from about 7 nm to about 20 nm, fromabout 7 nm to about 15 nm, from about 7 nm to about 12 nm or from about7 nm to about 10 nm, and all ranges and sub-ranges therebetween.

The additional coating 140 may include a scratch resistant layer orlayers. In some embodiments, the additional coating 140 includes acombination of easy-to-clean material and scratch resistant material. Inone example, the combination includes an easy-to-clean material anddiamond-like carbon. Such additional coatings 140 may have a thicknessin the range from about 5 nm to about 20 nm. The constituents of theadditional coating 140 may be provided in separate layers. For example,the diamond-like carbon may be disposed as a first layer and the easy-toclean can be disposed as a second layer on the first layer ofdiamond-like carbon. The thicknesses of the first layer and the secondlayer may be in the ranges provided above for the additional coating.For example, the first layer of diamond-like carbon may have a thicknessof about 1 nm to about 20 nm or from about 4 nm to about 15 nm (or morespecifically about 10 nm) and the second layer of easy-to-clean may havea thickness of about 1 nm to about 10 nm (or more specifically about 6nm). The diamond-like coating may include tetrahedral amorphous carbon(Ta—C), Ta—C:H, and/or a-C—H.

As mentioned herein, the optical coating 120 may include a scratchresistant layer 150 or coating (when a plurality of scratch resistantlayers are utilized), which may be disposed between the anti-reflectivecoating 130 and the substrate 110. In some embodiment, the scratchresistant layer 150 or coating is disposed between the layers of theanti-reflective coating 130 (such as 150 as shown in FIG. 7 or 345 asshown in FIG. 8). The two sections of the anti-reflective coating (i.e.,a first section disposed between the scratch resistant layer 150 and thesubstrate 110, and a second section disposed on the scratch resistantlayer) may have a different thickness from one another or may haveessentially the same thickness as one another. The layers of the twosections of the anti-reflective coating may be the same in composition,order, thickness and/or arrangement as one another or may differ fromone another.

Exemplary materials used in the scratch resistant layer 150 or coating(or the scratch-resistant layer/coating used as an additional coating140) may include an inorganic carbide, nitride, oxide, diamond-likematerial, or combination of these. Examples of suitable materials forthe scratch resistant layer or coating include metal oxides, metalnitrides, metal oxynitride, metal carbides, metal oxycarbides, and/orcombinations thereof combination thereof. Exemplary metals include B,Al, Si, Ti, V, Cr, Y, Zr, Nb, Mo, Sn, Hf, Ta and W. Specific examples ofmaterials that may be utilized in the scratch resistant layer or coatingmay include Al₂O₃, MN, AlO_(x)N_(y), Si₃N₄, SiO_(x)N_(y),Si_(u)Al_(v)O_(x)N_(y), diamond, diamond-like carbon, Si_(x)C_(y),Si_(x)O_(y)C_(z), ZrO₂, TiO_(x)N_(y) and combinations thereof. Thescratch resistant layer or coating may also comprise nanocompositematerials, or materials with a controlled microstructure to improvehardness, toughness, or abrasion/wear resistance. For example thescratch resistant layer or coating may comprise nanocrystallites in thesize range from about 5 nm to about 30 nm. In embodiments, the scratchresistant layer or coating may comprise transformation-toughenedzirconia, partially stabilized zirconia, or zirconia-toughened alumina.In embodiments, the scratch resistant layer or coating exhibits afracture toughness value greater than about 1 MPa√m and simultaneouslyexhibits a hardness value greater than about 8 GPa.

The scratch resistant layer may include a single layer 150 (as shown inFIG. 7), multiple sub-layers or sub-layers or single layers that exhibita refractive index gradient 345 (as shown in FIG. 8). Where multiplelayers are used, such layers form a scratch resistant coating 845. Forexample, a scratch resistant coating 845 may include a compositionalgradient of Si_(u)Al_(v)O_(x)N_(y) where the concentration of any one ormore of Si, Al, O and N are varied to increase or decrease therefractive index. The refractive index gradient may also be formed usingporosity. Such gradients are more fully described in U.S. patentapplication Ser. No. 14/262,224, entitled “Scratch-Resistant Articleswith a Gradient Layer”, filed on Apr. 28, 2014, which is herebyincorporated by reference in its entirety.

The composition of the scratch resistant layer or coating may bemodified to provide specific properties (e.g., hardness). In one or moreembodiments, the scratch resistant layer or coating exhibits a maximumhardness in the range from about 5 GPa to about 30 GPa as measured on amajor surface of the scratch resistant layer or coating, by theBerkovitch Indenter Hardness Test. In one or more embodiments, thescratch resistant layer or coating exhibits a maximum hardness in therange from about 6 GPa to about 30 GPa, from about 7 GPa to about 30GPa, from about 8 GPa to about 30 GPa, from about 9 GPa to about 30 GPa,from about 10 GPa to about 30 GPa, from about 12 GPa to about 30 GPa,from about 5 GPa to about 28 GPa, from about 5 GPa to about 26 GPa, fromabout 5 GPa to about 24 GPa, from about 5 GPa to about 22 GPa, fromabout 5 GPa to about 20 GPa, from about 12 GPa to about 25 GPa, fromabout 15 GPa to about 25 GPa, from about 16 GPa to about 24 GPa, fromabout 18 GPa to about 22 GPa and all ranges and sub-ranges therebetween.In one or more embodiments, the scratch resistant coating may exhibit amaximum hardness that is greater than 15 GPa, greater than 20 GPa, orgreater than 25 GPa. In one or more embodiments, the scratch resistantlayer exhibits a maximum hardness in the range from about 15 GPa toabout 150 GPa, from about 15 GPa to about 100 GPa, or from about 18 GPato about 100 GPa. Maximum hardness is the highest hardness valuemeasured over a range of indentation depths. Such maximum hardnessvalues are exhibited along an indentation depth of about 50 nm orgreater or 100 nm or greater (e.g., from about 100 nm to about 300 nm,from about 100 nm to about 400 nm, from about 100 nm to about 500 nm,from about 100 nm to about 600 nm, from about 200 nm to about 300 nm,from about 200 nm to about 400 nm, from about 200 nm to about 500 nm, orfrom about 200 nm to about 600 nm).

The physical thickness of the scratch resistant coating or layer may bein the range from about 1 nm to about 5 μm. In some embodiments, thephysical thickness of the scratch resistant coating may be in the rangefrom about 1 nm to about 3 μm, from about 1 nm to about 2.5 μm, fromabout 1 nm to about 2 μm, from about 1 nm to about 1.5 μm, from about 1nm to about 1 μm, from about 1 nm to about 0.5 μm, from about 1 nm toabout 0.2 μm, from about 1 nm to about 0.1 μm, from about 1 nm to about0.05 μm, from about 5 nm to about 0.05 μm, from about 10 nm to about0.05 μm, from about 15 nm to about 0.05 μm, from about 20 nm to about0.05 μm, from about 5 nm to about 0.05 μm, from about 200 nm to about 3μm, from about 400 nm to about 3 μm, from about 800 nm to about 3 μm,and all ranges and sub-ranges therebetween. In some embodiments, thephysical thickness of the scratch resistant coating may be in the rangefrom about 1 nm to about 25 nm. In some instances, the scratch-resistantlayer may include a nitride or an oxy-nitride material and may have athickness of about 200 nm or greater, 500 nm or greater or about 1000 nmor greater.

The article of one or more embodiments may be described as abrasionresistant as measured by various methods, after being abraded on theanti-reflective surface 122 according to a Taber Test after at leastabout 500 cycles. Various forms of abrasion test are known in the art,such as the test method specified in ASTM D1044-99, using abrasive mediasupplied by Taber Industries. Modified abrasion methods related to ASTMD1044-99 can be created using different types of abrading media,abradant geometry and motion, pressure, etc. in order to providerepeatable and measurable abrasion or wear tracks to meaningfullydifferentiate the abrasion resistance of different samples. For example,different test conditions will usually be appropriate for soft plasticsvs. hard inorganic test samples. The embodiments described herein weresubjected to a Taber Test, as defined herein, which is a specificmodified version of ASTM D1044-99 that gives clear and repeatabledifferentiation of durability between different samples which compriseprimarily hard inorganic materials, such as oxide glasses and oxide ornitride coatings. As used herein, the phrase “Taber Test” refers to atest method using a Taber Linear Abraser 5750 (TLA 5750) and accessoriessupplied by Taber Industries, in an environment including a temperatureof about 22° C.±3° C. and Relative Humidity of up to about 70%. The TLA5750 includes a CS-17 abraser material having a 6.7 mm diameter abraserhead. Each sample was abraded according to the Taber Test and theabrasive damage was evaluated using both Haze and BidirectionalTransmittance Distribution Function (CCBTDF) measurements, among othermethods. In the Taber Test, the procedure for abrading each sampleincludes placing the TLA 5750 and a flat sample support on a rigid, flatsurface and securing the TLA 5750 and the sample support to the surface.Before each sample is abraded under the Taber Test, the abraser isrefaced using a new S-14 refacing strip adhered to glass. The abraser issubjected to 10 refacing cycles using a cycle speed of 25 cycles/minuteand stroke length of 1 inch, with no additional weight added (i.e., atotal weight of about 350 g is used during refacing, which is thecombined weight of the spindle and collet holding the abraser). Theprocedure then includes operating the TLA 5750 to abrade the sample,where the sample is placed in the sample support in contact with theabraser head and supporting the weight applied to the abraser head,using a cycle speed of 25 cycles/minute, and a stroke length of 1 inch,and a weight such that the total weight applied to the sample is 850 g(i.e., a 500 g auxiliary weight is applied in addition to the 350 gcombined weight of the spindle and collet). The procedure includesforming two wear tracks on each sample for repeatability, and abradingeach sample for 500 cycle counts in each of the two wear tracks on eachsample.

In one or more embodiments, the anti-reflective surface 122 of thearticle 100 is abraded according to the above Taber Test and the articleexhibits a haze of about 10% of less, as measured on the abraded sideusing a hazemeter supplied by BYK Gardner under the trademark Haze-GardPlus®, using an aperture over the source port, the aperture having adiameter of 8 mm.

The article 100 of one or more embodiments exhibits such abrasionresistance with and without any additional coatings (including theadditional coating 140, which will be described herein). In someembodiments, the haze may be about 9% or less, about 8% or less, about7% or less, about 6% or less, about 5% or less, about 4% or less, about3% or less, about 2% or less, about 1% or less, about 0.5% or less orabout 0.3% or less. In some specific embodiments, the article 100exhibits a haze in the range from about 0.1% to about 10%, from about0.1% to about 9%, from about 0.1% to about 8%, from about 0.1% to about7%, from about 0.1% to about 6%, from about 0.1% to about 5%, from about0.1% to about 4%, from about 0.1% to about 3%, from about 0.1% to about2%, from about 0.1% to about 1%, 0.3% to about 10%, from about 0.5% toabout 10%, from about 1% to about 10%, from about 2% to about 10%, fromabout 3% to about 10%, from about 4% to about 10%, from about 5% toabout 10%, from about 6% to about 10%, from about 7% to about 10%, fromabout 1% to about 8%, from about 2% to about 6%, from about 3% to about5%, and all ranges and sub-ranges therebetween.

Alternate methods for quantifying the abrasion resistance are alsocontemplated here. In one or more embodiments, article 100 abraded bythe Taber Test on the anti-reflective surface 122 may exhibit anabrasion resistance as measured by atomic force microscopy (AFM) surfaceprofiling, which may be carried out for example over an 80×80 micronarea, or multiple 80×80 micron areas (to sample a larger portion of theabraded area) of the anti-reflective surface 122. From these AFM surfacescans, surface roughness statistics such as RMS roughness, Ra roughness,and peak-to-valley surface height may be evaluated. In one or moreembodiments, the article 100 (or specifically, the anti-reflectivesurface 122) may exhibit average surface roughness (Ra) values of about50 nm or less, about 25 nm or less, about 12 nm or less, about 10 nm orless, or about 5 nm or less, after being abraded under the Taber Testdescribed above.

In one or more embodiments, the article 100 may exhibit an abrasionresistance, after the anti-reflective surface 122 is abraded by theTaber Test as measured by a light scattering measurement. In one or moreembodiments, the light scattering measurement includes a bi-directionalreflectance distribution function (BRDF) or bi-directional transmittancedistribution function (BTDF) measurement carried out using a RadiantZemax IS-SA™ instrument. This instrument has the flexibility to measurelight scattering using any input angle from normal to about 85 degreesincidence in reflection, and from normal to about 85 degrees incidencein transmission, while also capturing all scattered light output ineither reflection or transmission into 2*Pi steradians (a fullhemisphere in reflection or transmission). In one embodiment, thearticle 100 exhibits an abrasion resistance, as measured using BTDF atnormal incidence and analyzing the transmitted scattered light at aselected angular range, for example from about 10° to about 80° degreesin polar angles and any angular range therein. The full azimuthal rangeof angles can be analyzed and integrated, or particular azimuthalangular slices can be selected, for example from about 0° and 90°azimuthally. In the case of linear abrasion, it may be desired to choosean azimuthal direction that is substantially orthogonal to the abrasiondirection so as to increase signal-to-noise of the optical scatteringmeasurement. In one or more embodiments, the article 100 may exhibit ascattered light intensity as measured at the anti-reflective coating120, of about less than about 0.1, about 0.05 or less, about 0.03 orless, about 0.02 or less, about 0.01 or less, about 0.005 or less, orabout 0.003 or less (in units of 1/steradian), when using the RadiantZemax IS-SA tool in CCBTDF mode at normal incidence in transmission,with a 2 mm aperture and a monochrometer set to 600 nm wavelength, andwhen evaluated at polar scattering angles in the range from about 15° toabout 60° (e.g. specifically, about 20° or about 40°). Normal incidencein transmission may be otherwise known as zero degrees in transmission,which may be denoted as 180° incidence by the instrument software. Inone or more embodiments, the scattered light intensity may be measuredalong an azimuthal direction substantially orthogonal to the abradeddirection of a sample abraded by the Taber Test. In one example, theTaber Test may use from about 10 cycles to about 1000 cycles, and allvalues in between. These optical intensity values may also correspond toless than about 1%, less than about 0.5%, less than about 0.2%, or lessthan about 0.1% of the input light intensity that is scattered intopolar scattering angles greater than about 5 degrees, greater than about10 degrees, greater than about 30 degrees, or greater than about 45degrees.

Generally speaking, BTDF testing at normal incidence, as describedherein, is closely related to the transmission haze measurement, in thatboth are measuring the amount of light that is scattered in transmissionthrough a sample (or, in this case the article 100, after abrading theanti-reflective coating 120). BTDF measurements provide more sensitivityas well as more detailed angular information, compared to hazemeasurements. BTDF allows measurement of scattering into different polarand azimuthal angles, for example allowing us to selectively evaluatethe scattering into azimuthal angles that are substantially orthogonalto the abrasion direction in the linear Taber test (these are the angleswhere light scattering from linear abrasion is the highest).Transmission haze is essentially the integration of all scattered lightmeasured by normal incidence BTDF into the entire hemisphere of polarangles greater than about +/−2.5 degrees.

The optical coating 120 and the article 100 may be described in terms ofa hardness measured by a Berkovich Indenter Hardness Test. As usedherein, the “Berkovich Indenter Hardness Test” includes measuring thehardness of a material on a surface thereof by indenting the surfacewith a diamond Berkovich indenter. The Berkovich Indenter Hardness Testincludes indenting the anti-reflective surface 122 of the article or thesurface of the optical coating 120 (or the surface of any one or more ofthe layers in the anti-reflective coating) with the diamond Berkovichindenter to form an indent to an indentation depth in the range fromabout 50 nm to about 1000 nm (or the entire thickness of theanti-reflective coating or layer, whichever is less) and measuring themaximum hardness from this indentation along the entire indentationdepth range or a segment of this indentation depth (e.g., in the rangefrom about 100 nm to about 600 nm), generally using the methods setforth in Oliver, W. C.; Pharr, G. M. An improved technique fordetermining hardness and elastic modulus using load and displacementsensing indentation experiments. J. Mater. Res., Vol. 7, No. 6, 1992,1564-1583; and Oliver, W. C.; Pharr, G. M. Measurement of Hardness andElastic Modulus by Instrument Indentation: Advances in Understanding andRefinements to Methodology. J. Mater. Res., Vol. 19, No. 1, 2004, 3-20.As used herein, hardness refers to a maximum hardness, and not anaverage hardness.

Typically, in nanoindentation measurement methods (such as by using aBerkovich indenter) of a coating that is harder than the underlyingsubstrate, the measured hardness may appear to increase initially due todevelopment of the plastic zone at shallow indentation depths and thenincreases and reaches a maximum value or plateau at deeper indentationdepths. Thereafter, hardness begins to decrease at even deeperindentation depths due to the effect of the underlying substrate. Wherea substrate having an increased hardness compared to the coating isutilized, the same effect can be seen; however, the hardness increasesat deeper indentation depths due to the effect of the underlyingsubstrate.

The indentation depth range and the hardness values at certainindentation depth range(s) can be selected to identify a particularhardness response of the optical film structures and layers thereof,described herein, without the effect of the underlying substrate. Whenmeasuring hardness of the optical film structure (when disposed on asubstrate) with a Berkovich indenter, the region of permanentdeformation (plastic zone) of a material is associated with the hardnessof the material. During indentation, an elastic stress field extendswell beyond this region of permanent deformation. As indentation depthincreases, the apparent hardness and modulus are influenced by stressfield interactions with the underlying substrate. The substrateinfluence on hardness occurs at deeper indentation depths (i.e.,typically at depths greater than about 10% of the optical film structureor layer thickness). Moreover, a further complication is that thehardness response requires a certain minimum load to develop fullplasticity during the indentation process. Prior to that certain minimumload, the hardness shows a generally increasing trend.

At small indentation depths (which also may be characterized as smallloads) (e.g., up to about 50 nm), the apparent hardness of a materialappears to increase dramatically versus indentation depth. This smallindentation depth regime does not represent a true metric of hardnessbut instead, reflects the development of the aforementioned plasticzone, which is related to the finite radius of curvature of theindenter. At intermediate indentation depths, the apparent hardnessapproaches maximum levels. At deeper indentation depths, the influenceof the substrate becomes more pronounced as the indentation depthsincrease. Hardness may begin to drop dramatically once the indentationdepth exceeds about 30% of the optical film structure thickness or thelayer thickness.

FIG. 21 illustrates the changes in measured hardness value as a functionof indentation depth and thickness of a coating. As shown in FIG. 21,the hardness measured at intermediate indentation depths (at whichhardness approaches and is maintained at maximum levels) and at deeperindentation depths depends on the thickness of a material or layer. FIG.21 illustrates the hardness response of four different layers ofAlO_(x)N_(y) having different thicknesses. The hardness of each layerwas measured using the Berkovich Indenter Hardness Test. The 500nm-thick layer exhibited its maximum hardness at indentation depths fromabout 100 nm to 180 nm, followed by a dramatic decrease in hardness atindentation depths from about 180 nm to about 200 nm, indicating thehardness of the substrate influencing the hardness measurement. The 1000nm-thick layer exhibited a maximum hardness at indentation depths fromabout 100 nm to about 300 nm, followed by a dramatic decrease inhardness at indentation depths greater than about 300 nm. The 1500nm-thick layer exhibited a maximum hardness at indentation depths fromabout 100 nm to about 550 nm and the 2000-nm thick layer exhibited amaximum hardness at indentation depths from about 100 nm to about 600nm. Although FIG. 21 illustrates a thick single layer, the same behavioris observed in thinner coatings and those including multiple layers suchas the anti-reflective coating 120 of the embodiments described herein.

In some embodiments, the optical 120 may exhibit a hardness of about 8GPa or greater, about 10 GPa or greater or about 12 GPa or greater(e.g., 14 GPa or greater, 16 GPa or greater, 18 GPa or greater, 20 GPaor greater). The hardness of the optical coating 120 may be up to about20 GPa or 30 GPa. The article 100, including the anti-reflective coating120 and any additional coatings, as described herein, exhibit a hardnessof about 5 GPa or greater, about 8 GPa or greater, about 10 GPa orgreater or about 12 GPa or greater (e.g., 14 GPa or greater, 16 GPa orgreater, 18 GPa or greater, 20 GPa or greater), as measured on theanti-reflective surface 122, by a Berkovitch Indenter Hardness Test. Thehardness of the optical 120 may be up to about 20 GPa or 30 GPa. Suchmeasured hardness values may be exhibited by the optical coating 120and/or the article 100 along an indentation depth of about 50 nm orgreater or about 100 nm or greater (e.g., from about 100 nm to about 300nm, from about 100 nm to about 400 nm, from about 100 nm to about 500nm, from about 100 nm to about 600 nm, from about 200 nm to about 300nm, from about 200 nm to about 400 nm, from about 200 nm to about 500nm, or from about 200 nm to about 600 nm). In one or more embodiments,the article exhibits a hardness that is greater than the hardness of thesubstrate (which can be measured on the opposite surface from theanti-reflective surface).

The optical coating 120 may have at least one layer having a hardness(as measured on the surface of such layer, e.g., surface of the secondhigh RI layer 130B of FIG. 2 or the surface of the scratch resistantlayer) of about 12 GPa or greater, about 13 GPa or greater, about 14 GPaor greater, about 15 GPa or greater, about 16 GPa or greater, about 17GPa or greater, about 18 GPa or greater, about 19 GPa or greater, about20 GPa or greater, about 22 GPa or greater, about 23 GPa or greater,about 24 GPa or greater, about 25 GPa or greater, about 26 GPa orgreater, or about 27 GPa or greater (up to about 50 GPa), as measured bythe Berkovich Indenter Hardness Test. The hardness of such layer may bein the range from about 18 GPa to about 21 GPa, as measured by theBerkovich Indenter Hardness Test. Such measured hardness values may beexhibited by the at least one layer along an indentation depth of about50 nm or greater or 100 nm or greater (e.g., from about 100 nm to about300 nm, from about 100 nm to about 400 nm, from about 100 nm to about500 nm, from about 100 nm to about 600 nm, from about 200 nm to about300 nm, from about 200 nm to about 400 nm, from about 200 nm to about500 nm, or from about 200 nm to about 600 nm).

In one or more embodiments, the optical coating 120 or individual layerswithin the optical coating may exhibit an elastic modulus of about 75GPa or greater, about 80 GPa or greater or about 85 GPa or greater, asmeasured on the anti-reflective surface 122, by indenting that surfacewith a Berkovitch indenter. These modulus values may represent a modulusmeasured very close to the anti-reflective surface, e.g. at indentationdepths of 0 nm to about 50 nm, or it may represent a modulus measured atdeeper indentation depths, e.g. from about 50 nm to about 1000 nm.

In embodiments of the article which include a scratch-resistant layer(when used as part of the anti-reflective coating, e.g., 150 of FIG. 7or 345 of FIG. 8) or scratch resistant coating (when used as anadditional coating 140), the article may exhibit a maximum hardness inthe range from about 12 GPa to about 25 GPa, as measured by theBerkovich Indenter Hardness Test on the anti-reflective surface 122, orthe surface of the scratch resistant coating, respectively. Suchmeasured hardness values may be exhibited along an indentation depth ofabout 50 nm or greater or 100 nm or greater (e.g., from about 100 nm toabout 300 nm, from about 100 nm to about 400 nm, from about 100 nm toabout 500 nm, from about 100 nm to about 600 nm, from about 200 nm toabout 300 nm, from about 200 nm to about 400 nm, from about 200 nm toabout 500 nm, or from about 200 nm to about 600 nm). This hardness maybe exhibited even when the scratch resistant layer is not disposed at ornear the anti-reflective surface 122 (e.g., as shown in FIGS. 7 and 8).

Optical interference between reflected waves from the optical coating120/air interface and the optical coating 120/substrate 110 interfacecan lead to spectral reflectance and/or transmittance oscillations thatcreate apparent color in the article 100. As used herein, the term“transmittance” is defined as the percentage of incident optical powerwithin a given wavelength range transmitted through a material (e.g.,the article, the substrate or the optical film or portions thereof). Theterm “reflectance” is similarly defined as the percentage of incidentoptical power within a given wavelength range that is reflected from amaterial (e.g., the article, the substrate, or the optical film orportions thereof). Transmittance and reflectance are measured using aspecific linewidth. In one or more embodiments, the spectral resolutionof the characterization of the transmittance and reflectance is lessthan 5 nm or 0.02 eV. The color may be more pronounced in reflection.The angular color shifts in reflection with viewing angle due to a shiftin the spectral reflectance oscillations with incident illuminationangle. Angular color shifts in transmittance with viewing angle are alsodue to the same shift in the spectral transmittance oscillation withincident illumination angle. The observed color and angular color shiftswith incident illumination angle are often distracting or objectionableto device users, particularly under illumination with sharp spectralfeatures such as fluorescent lighting and some LED lighting. Angularcolor shifts in transmission may also play a factor in color shift inreflection and vice versa. Factors in angular color shifts intransmission and/or reflection may also include angular color shifts dueto viewing angle or angular color shifts away from a certain white pointthat may be caused by material absorption (somewhat independent ofangle) defined by a particular illuminant or test system.

The oscillations may be described in terms of amplitude. As used herein,the term “amplitude” includes the peak-to-valley change in reflectanceor transmittance. The phrase “average amplitude” includes thepeak-to-valley change in reflectance or transmittance averaged overseveral oscillation cycles or wavelength sub-ranges within the opticalwavelength regime. As used herein, the “optical wavelength regime”includes the wavelength range from about 400 nm to about 800 nm (andmore specifically from about 450 nm to about 650 nm).

The embodiments of this disclosure include an anti-reflective coating toprovide improved optical performance, in terms of colorlessness and/orsmaller angular color shifts with viewed at varying incidentillumination angles from normal incidence under different illuminants.

One aspect of this disclosure pertains to an article that exhibitscolorlessness in reflectance and/or transmittance even when viewed atdifferent incident illumination angles under an illuminant. In one ormore embodiments, the article exhibits an angular color shift inreflectance and/or transmittance of about 5 or less or about 2 or lessbetween a reference illumination angle and any incidental illuminationangles in the ranges provided herein. As used herein, the phrase “colorshift” (angular or reference point) refers to the change in both a* andb*, under the CIE L*, a*, b* colorimetry system in reflectance and/ortransmittance. It should be understood that unless otherwise noted, theL* coordinate of the articles described herein are the same at any angleor reference point and do not influence color shift. For example,angular color shift may be determined using the following Equation (1):

√((a* ₂ −a* ₁)²+(b* ₂ −b* ₁)²),  (1)

with a*₁, and b*₁ representing the a* and b* coordinates of the articlewhen viewed at incidence reference illumination angle (which may includenormal incidence) and a*₂, and b*₂ representing the a* and b*coordinates of the article when viewed at an incident illuminationangle, provided that the incident illumination angle is different fromthe reference illumination angle and in some cases differs from thereference illumination angle by at least about 1 degree, 2 degrees orabout 5 degrees. In some instances, an angular color shift inreflectance and/or transmittance of about 10 or less (e.g., 5 or less, 4or less, 3 or less, or 2 or less) is exhibited by the article whenviewed at various incident illumination angles from a referenceillumination angle, under an illuminant. In some instances the angularcolor shift in reflectance and/or transmittance is about 1.9 or less,1.8 or less, 1.7 or less, 1.6 or less, 1.5 or less, 1.4 or less, 1.3 orless, 1.2 or less, 1.1 or less, 1 or less, 0.9 or less, 0.8 or less, 0.7or less, 0.6 or less, 0.5 or less, 0.4 or less, 0.3 or less, 0.2 orless, or 0.1 or less. In some embodiments, the angular color shift maybe about 0. The illuminant can include standard illuminants asdetermined by the CIE, including A illuminants (representingtungsten-filament lighting), B illuminants (daylight simulatingilluminants), C illuminants (daylight simulating illuminants), D seriesilluminants (representing natural daylight), and F series illuminants(representing various types of fluorescent lighting). In specificexamples, the articles exhibit an angular color shift in reflectanceand/or transmittance of about 2 or less when viewed at incidentillumination angle from the reference illumination angle under a CIE F2,F10, F11, F12 or D65 illuminant, or more specifically, under a CIE F2illuminant.

The reference illumination angle may include normal incidence (i.e.,from about 0 degrees to about 10 degrees), or 5 degrees from normalincidence, 10 degrees from normal incidence, 15 degrees from normalincidence, 20 degrees from normal incidence, 25 degrees from normalincidence, 30 degrees from normal incidence, 35 degrees from normalincidence, 40 degrees from normal incidence, 50 degrees from normalincidence, 55 degrees from normal incidence, or 60 degrees from normalincidence, provided the difference between the reference illuminationangle and the difference between the incident illumination angle and thereference illumination angle is at least about 1 degree, 2 degrees orabout 5 degrees. The incident illumination angle may be, with respect tothe reference illumination angle, in the range from about 5 degrees toabout 80 degrees, from about 5 degrees to about 70 degrees, from about 5degrees to about 65 degrees, from about 5 degrees to about 60 degrees,from about 5 degrees to about 55 degrees, from about 5 degrees to about50 degrees, from about 5 degrees to about 45 degrees, from about 5degrees to about 40 degrees, from about 5 degrees to about 35 degrees,from about 5 degrees to about 30 degrees, from about 5 degrees to about25 degrees, from about 5 degrees to about 20 degrees, from about 5degrees to about 15 degrees, and all ranges and sub-ranges therebetween,away from the reference illumination angle. The article may exhibit theangular color shifts in reflectance and/or transmittance describedherein at and along all the incident illumination angles in the rangefrom about 2 degrees to about 80 degrees (or from about 10 degrees toabout 80 degrees, or from about 20 degrees to about 80 degrees), whenthe reference illumination angle is normal incidence. In someembodiments, the article may exhibit the angular color shifts inreflectance and/or transmittance described herein at and along all theincident illumination angles in the range from about 2 degrees to about80 degrees (or from about 10 degrees to about 80 degrees, or from about20 degrees to about 80 degrees), when the difference between theincident illumination angle and the reference illumination angle is atleast about 1 degree, 2 degrees or about 5 degrees. In one example, thearticle may exhibit an angular color shift in reflectance and/ortransmittance of 5 or less (e.g., 4 or less, 3 or less or about 2 orless) at any incident illumination angle in the range from about 2degrees to about 60 degrees, from about 5 degrees to about 60 degrees,or from about 10 degrees to about 60 degrees away from a referenceillumination angle equal to normal incidence. In other examples, thearticle may exhibit an angular color shift in reflectance and/ortransmittance of 5 or less (e.g., 4 or less, 3 or less or about 2 orless) when the reference illumination angle is 10 degrees and theincident illumination angle is any angle in the range from about 12degrees to about 60 degrees, from about 15 degrees to about 60 degrees,or from about 20 degrees to about 60 degrees away from the referenceillumination angle.

In some embodiments, the angular color shift may be measured at allangles between a reference illumination angle (e.g., normal incidence)and an incident illumination angle in the range from about 20 degrees toabout 80 degrees. In other words, the angular color shift may bemeasured and may be less than about 5 or less than about 2, at allangles in the range from about 0 degrees and 20 degrees, from about 0degrees to about 30 degrees, from about 0 degrees to about 40 degrees,from about 0 degrees to about 50 degrees, from about 0 degrees to about60 degrees or from about 0 degrees to about 80 degrees.

In one or more embodiments, the article exhibits a color in the CIE L*,a*, b* colorimetry system in reflectance and/or transmittance such thatthe distance or reference point color shift between the transmittancecolor or reflectance coordinates from a reference point is less thanabout 5 or less than about 2 under an illuminant (which can includestandard illuminants as determined by the CIE, including A illuminants(representing tungsten-filament lighting), B illuminants (daylightsimulating illuminants), C illuminants (daylight simulatingilluminants), D series illuminants (representing natural daylight), andF series illuminants (representing various types of fluorescentlighting)). In specific examples, the articles exhibit a color shift inreflectance and/or transmittance of about 2 or less when viewed atincident illumination angle from the reference illumination angle undera CIE F2, F10, F11, F12 or D65 illuminant or more specifically under aCIE F2 illuminant. Stated another way, the article may exhibit atransmittance color (or transmittance color coordinates) and/or areflectance color (or reflectance color coordinates) measured at theanti-reflective surface 122 having a reference point color shift of lessthan about 2 from a reference point, as defined herein. Unless otherwisenoted, the transmittance color or transmittance color coordinates aremeasured on two surfaces of the article including at the anti-reflectivesurface 122 and the opposite bare surface of the article (i.e., 114).Unless otherwise noted, the reflectance color or reflectance colorcoordinates are measured on only the anti-reflective surface 122 of thearticle. However, the reflectance color or reflectance color coordinatesdescribed herein can be measured on both the anti-reflective surface 122of the article and the opposite side of the article (i.e., major surface114 in FIG. 1) using either a 2-surface measurement (reflections fromtwo sides of an article are both included) or a 1-surface measurement(reflection only from the anti-reflective surface 122 of the article ismeasured). Of these, the 1-surface reflectance measurement is typicallythe more challenging metric to achieve low color or low-color shiftvalues for anti-reflective coatings, and this has relevance toapplications (such as smartphones, etc.) where the back surface of thearticle is bonded to a light absorbing medium such as black ink or anLCD or OLED device).

In one or more embodiments, the reference point may be the origin (0, 0)in the CIE L*, a*, b* colorimetry system (or the color coordinates a*=0,b*=0), the coordinates (a*=−2,b*=−2), or the transmittance orreflectance color coordinates of the substrate. It should be understoodthat unless otherwise noted, the L* coordinate of the articles describedherein are the same as the reference point and do not influence colorshift. Where the reference point color shift of the article is definedwith respect to the substrate, the transmittance color coordinates ofthe article are compared to the transmittance color coordinates of thesubstrate and the reflectance color coordinates of the article arecompared to the reflectance color coordinates of the substrate.

In one or more specific embodiments, the reference point color shift ofthe transmittance color and/or the reflectance color may be less than 1or even less than 0.5. In one or more specific embodiments, thereference point color shift for the transmittance color and/or thereflectance color may be 1.8, 1.6, 1.4, 1.2, 0.8, 0.6, 0.4, 0.2, 0 andall ranges and sub-ranges therebetween. Where the reference point is thecolor coordinates a*=0, b*=0, the reference point color shift iscalculated by Equation (2).

reference point color shift=√((a* _(article))²(b* _(article))²)  (2)

Where the reference point is the color coordinates a*=−2, b*=−2, thereference point color shift is calculated by Equation (3).

reference point color shift=√((a* _(article)+2)²+(b*_(article)+2)²)  (3)

Where the reference point is the color coordinates of the substrate, thereference point color shift is calculated by Equation (4).

reference point color shift=√((a* _(article) −a* _(substrate))²(b*_(article) −b* _(substrate))²)  (4)

In some embodiments, the article may exhibit a transmittance color (ortransmittance color coordinates) and a reflectance color (or reflectancecolor coordinates) such that the reference point color shift is lessthan 2 when the reference point is any one of the color coordinates ofthe substrate, the color coordinates a*=0, b*=0 and the coordinatesa*=−2, b*=−2.

In one or more embodiment, the article may exhibit a b* value inreflectance (as measured at the anti-reflective surface only) in therange from about −5 to about 1, from about −5 to about 0, from about −4to about 1, or from about −4 to about 0, in the CIE L*, a*, b*colorimetry system at all incidence illumination angles in the rangefrom about 0 to about 60 degrees (or from about 0 degrees to about 40degrees or from about 0 degrees to about 30 degrees).

In one or more embodiment, the article may exhibit a b* value intransmittance (as measured at the anti-reflective surface and theopposite bare surface of the article) of less than about 2 (or about 1.8or less, about 1.6 or less, 1.5 or less, 1.4 or less, 1.2 or less, orabout 1 or less) in the CIE L*, a*, b* colorimetry system at allincidence illumination angles in the range from about 0 to about 60degrees (or from about 0 degrees to about 40 degrees or from about 0degrees to about 30 degrees). The lower limit of the b* value intransmittance may be about −5.

In some embodiments, the article exhibits an a* value in transmittance(at the anti-reflective surface and the opposite bare surface) in therange from about −1.5 to about 1.5 (e.g., −1.5 to −1.2, −1.5 to −1, −1.2to 1.2, −1 to 1, −1 to 0.5, or −1 to 0) at incident illumination anglesin the range from about 0 degrees to about 60 degrees under illuminantsD65, A, and F2. In some embodiments, the article exhibits a b* value intransmittance (at the anti-reflective surface and the opposite baresurface) in the range from about −1.5 to about 1.5 (e.g., −1.5 to −1.2,−1.5 to −1, −1.2 to 1.2, −1 to 1, −1 to 0.5, or −1 to 0) at incidentillumination angles in the range from about 0 degrees to about 60degrees under illuminants D65, A, and F2.

In some embodiments, the article exhibits an a* value in reflectance (atonly the anti-reflective surface) in the range from about −5 to about 2(e.g., −4.5 to 1.5, −3 to 0, −2.5 to 0.25) at incident illuminationangles in the range from about 0 degrees to about 60 degrees underilluminants D65, A, and F2. In some embodiments, the article exhibits ab* value in reflectance (at only the anti-reflective surface) in therange from about −7 to about 0 at incident illumination angles in therange from about 0 degrees to about 60 degrees under illuminants D65, A,and F2.

The article of one or more embodiments, or the anti-reflective surface122 of one or more articles, may exhibit an average light transmittanceof about 95% or greater (e.g., about 9.5% or greater, about 96% orgreater, about 96.5% or greater, about 97% or greater, about 97.5% orgreater, about 98% or greater, about 98.5% or greater or about 99% orgreater) over the optical wavelength regime in the range from about 400nm to about 800 nm. In some embodiments, the article, or theanti-reflective surface 122 of one or more articles, may exhibit anaverage light reflectance of about 2% or less (e.g., about 1.5% or less,about 1% or less, about 0.75% or less, about 0.5% or less, or about0.25% or less) over the optical wavelength regime in the range fromabout 400 nm to about 800 nm. These light transmittance and lightreflectance values may be observed over the entire optical wavelengthregime or over selected ranges of the optical wavelength regime (e.g., a100 nm wavelength range, 150 nm wavelength range, a 200 nm wavelengthrange, a 250 nm wavelength range, a 280 nm wavelength range, or a 300 nmwavelength range, within the optical wavelength regime). In someembodiments, these light reflectance and transmittance values may be atotal reflectance or total transmittance (taking into accountreflectance or transmittance on both the anti-reflective surface 122 andthe opposite major surface 114) or may be observed on a single side ofthe article, as measured on the anti-reflective surface 122 only(without taking into account the opposite surface). Unless otherwisespecified, the average reflectance or transmittance is measured at anincident illumination angle in the range from about 0 degrees to about10 degrees (however, such measurements may be provided at incidentillumination angles of 45 degrees or 60 degrees).

In some embodiments, the article of one or more embodiments, or theanti-reflective surface 122 of one or more articles, may exhibit anaverage visible photopic reflectance of about 1% or less, about 0.7% orless, about 0.5% or less, or about 0.45% or less over the opticalwavelength regime. These photopic reflectance values may be exhibited atincident illumination angles in the range from about 0° to about 20°,from about 0° to about 40° or from about 0° to about 60°. As usedherein, photopic reflectance mimics the response of the human eye byweighting the reflectance versus wavelength spectrum according to thehuman eye's sensitivity. Photopic reflectance may also be defined as theluminance, or tristimulus Y value of reflected light, according to knownconventions such as CIE color space conventions. The average photopicreflectance is defined in Equation (4) as the spectral reflectance, R(λ)multiplied by the illuminant spectrum, (λ) and the CIE's color matchingfunction y(λ), related to the eye's spectral response:

$\begin{matrix}{{\langle R_{p}\rangle} = {\int\limits_{380\mspace{14mu} {nm}}^{720\mspace{14mu} {nm}}{{R(\lambda)} \times {I(\lambda)} \times {\overset{\_}{y}(\lambda)}{\lambda}}}} & (5)\end{matrix}$

In some embodiments, the article exhibits a single-side average photopicreflectance, measured at normal or near-normal incidence (e.g. 0-10degrees) on the anti-reflective surface only of less than about 10%. Insome embodiments, the single-side average photopic reflectance is about9% or less, about 8% or less, about 7% or less, about 6% or less, about5% or less, about 4% or less, about 3%, or about 2% or less. In aspecific embodiment, the anti-reflective surface 122 of one or morearticles (i.e. when measuring the anti-reflective surface only through asingle-sided measurement), may exhibit the above average photopicreflectance values, while simultaneously exhibiting a maximumreflectance color shift, over the entire incident illumination anglerange from about 5 degrees to about 60 degrees (with the referenceillumination angle being normal incidence) using D65 illumination and/orF2 illuminant, of less than about 5.0, less than about 4.0, less thanabout 3.0, less than about 2.0, less than about 1.5, or less than about1.25. These maximum reflectance color shift values represent the lowestcolor point value measured at any angle from about 5 degrees to about 60degrees from normal incidence, subtracted from the highest color pointvalue measured at any angle in the same range. The values may representa maximum change in a* value (a*_(highest)−a*lowest), a maximum changein b* value (b*_(highest)−b*_(lowest)), a maximum change in both a* andb* values, or a maximum change in the quantity√((a*_(highest)−a*_(lowest))²+(b*_(highest)−b*_(lowest))²).

Substrate

The substrate 110 may include an inorganic material and may include anamorphous substrate, a crystalline substrate or a combination thereof.The substrate 110 may be formed from man-made materials and/or naturallyoccurring materials (e.g., quartz and polymers). For example, in someinstances, the substrate 110 may be characterized as organic and mayspecifically be polymeric. Examples of suitable polymers include,without limitation: thermoplastics including polystyrene (PS) (includingstyrene copolymers and blends), polycarbonate (PC) (including copolymersand blends), polyesters (including copolymers and blends, includingpolyethyleneterephthalate and polyethyleneterephthalate copolymers),polyolefins (PO) and cyclicpolyolefins (cyclic-PO), polyvinylchloride(PVC), acrylic polymers including polymethyl methacrylate (PMMA)(including copolymers and blends), thermoplastic urethanes (TPU),polyetherimide (PEI) and blends of these polymers with each other. Otherexemplary polymers include epoxy, styrenic, phenolic, melamine, andsilicone resins.

In some specific embodiments, the substrate 110 may specifically excludepolymeric, plastic and/or metal substrates. The substrate may becharacterized as alkali-including substrates (i.e., the substrateincludes one or more alkalis). In one or more embodiments, the substrateexhibits a refractive index in the range from about 1.45 to about 1.55.In specific embodiments, the substrate 110 may exhibit an averagestrain-to-failure at a surface on one or more opposing major surfacethat is 0.5% or greater, 0.6% or greater, 0.7% or greater, 0.8% orgreater, 0.9% or greater, 1% or greater, 1.1% or greater, 1.2% orgreater, 1.3% or greater, 1.4% or greater 1.5% or greater or even 2% orgreater, as measured using ball-on-ring testing using at least 5, atleast 10, at least 15, or at least 20 samples. In specific embodiments,the substrate 110 may exhibit an average strain-to-failure at itssurface on one or more opposing major surface of about 1.2%, about 1.4%,about 1.6%, about 1.8%, about 2.2%, about 2.4%, about 2.6%, about 2.8%,or about 3% or greater.

Suitable substrates 110 may exhibit an elastic modulus (or Young'smodulus) in the range from about 30 GPa to about 120 GPa. In someinstances, the elastic modulus of the substrate may be in the range fromabout 30 GPa to about 110 GPa, from about 30 GPa to about 100 GPa, fromabout 30 GPa to about 90 GPa, from about 30 GPa to about 80 GPa, fromabout 30 GPa to about 70 GPa, from about 40 GPa to about 120 GPa, fromabout 50 GPa to about 120 GPa, from about 60 GPa to about 120 GPa, fromabout 70 GPa to about 120 GPa, and all ranges and sub-rangestherebetween.

In one or more embodiments, the amorphous substrate may include glass,which may be strengthened or non-strengthened. Examples of suitableglass include soda lime glass, alkali aluminosilicate glass, alkalicontaining borosilicate glass and alkali aluminoborosilicate glass. Insome variants, the glass may be free of lithia. In one or morealternative embodiments, the substrate 110 may include crystallinesubstrates such as glass ceramic substrates (which may be strengthenedor non-strengthened) or may include a single crystal structure, such assapphire. In one or more specific embodiments, the substrate 110includes an amorphous base (e.g., glass) and a crystalline cladding(e.g., sapphire layer, a polycrystalline alumina layer and/or or aspinel (MgAl₂O₄) layer).

The substrate 110 of one or more embodiments may have a hardness that isless than the hardness of the article (as measured by the BerkovichIndenter Hardness Test described herein). The hardness of the substratemay be measured using known methods in the art, including but notlimited to the Berkovich Indenter Hardness Test or Vickers hardnesstest.

The substrate 110 may be substantially planar or sheet-like, althoughother embodiments may utilize a curved or otherwise shaped or sculptedsubstrate. The substrate 110 may be substantially optically clear,transparent and free from light scattering. In such embodiments, thesubstrate may exhibit an average light transmission over the opticalwavelength regime of about 85% or greater, about 86% or greater, about87% or greater, about 88% or greater, about 89% or greater, about 90% orgreater, about 91% or greater or about 92% or greater. In one or morealternative embodiments, the substrate 110 may be opaque or exhibit anaverage light transmission over the optical wavelength regime of lessthan about 10%, less than about 9%, less than about 8%, less than about7%, less than about 6%, less than about 5%, less than about 4%, lessthan about 3%, less than about 2%, less than about 1%, or less thanabout 0%. In some embodiments, these light reflectance and transmittancevalues may be a total reflectance or total transmittance (taking intoaccount reflectance or transmittance on both major surfaces of thesubstrate) or may be observed on a single side of the substrate (i.e.,on the anti-reflective surface 122 only, without taking into account theopposite surface). Unless otherwise specified, the average reflectanceor transmittance is measured at an incident illumination angle of 0degrees (however, such measurements may be provided at incidentillumination angles of 45 degrees or 60 degrees). The substrate 110 mayoptionally exhibit a color, such as white, black, red, blue, green,yellow, orange etc.

Additionally or alternatively, the physical thickness of the substrate110 may vary along one or more of its dimensions for aesthetic and/orfunctional reasons. For example, the edges of the substrate 110 may bethicker as compared to more central regions of the substrate 110. Thelength, width and physical thickness dimensions of the substrate 110 mayalso vary according to the application or use of the article 100.

The substrate 110 may be provided using a variety of differentprocesses. For instance, where the substrate 110 includes an amorphoussubstrate such as glass, various forming methods can include float glassprocesses and down-draw processes such as fusion draw and slot draw.

Once formed, a substrate 110 may be strengthened to form a strengthenedsubstrate. As used herein, the term “strengthened substrate” may referto a substrate that has been chemically strengthened, for examplethrough ion-exchange of larger ions for smaller ions in the surface ofthe substrate. However, other strengthening methods known in the art,such as thermal tempering, or utilizing a mismatch of the coefficient ofthermal expansion between portions of the substrate to createcompressive stress and central tension regions, may be utilized to formstrengthened substrates.

Where the substrate is chemically strengthened by an ion exchangeprocess, the ions in the surface layer of the substrate are replacedby—or exchanged with—larger ions having the same valence or oxidationstate. Ion exchange processes are typically carried out by immersing asubstrate in a molten salt bath containing the larger ions to beexchanged with the smaller ions in the substrate. It will be appreciatedby those skilled in the art that parameters for the ion exchangeprocess, including, but not limited to, bath composition andtemperature, immersion time, the number of immersions of the substratein a salt bath (or baths), use of multiple salt baths, additional stepssuch as annealing, washing, and the like, are generally determined bythe composition of the substrate and the desired compressive stress(CS), depth of compressive stress layer (or depth of layer) of thesubstrate that result from the strengthening operation. By way ofexample, ion exchange of alkali metal-containing glass substrates may beachieved by immersion in at least one molten bath containing a salt suchas, but not limited to, nitrates, sulfates, and chlorides of the largeralkali metal ion. The temperature of the molten salt bath typically isin a range from about 380° C. up to about 450° C., while immersion timesrange from about 15 minutes up to about 40 hours. However, temperaturesand immersion times different from those described above may also beused.

In addition, non-limiting examples of ion exchange processes in whichglass substrates are immersed in multiple ion exchange baths, withwashing and/or annealing steps between immersions, are described in U.S.patent application Ser. No. 12/500,650, filed Jul. 10, 2009, by DouglasC. Allan et al., entitled “Glass with Compressive Surface for ConsumerApplications” and claiming priority from U.S. Provisional PatentApplication No. 61/079,995, filed Jul. 11, 2008, in which glasssubstrates are strengthened by immersion in multiple, successive, ionexchange treatments in salt baths of different concentrations; and U.S.Pat. No. 8,312,739, by Christopher M. Lee et al., issued on Nov. 20,2012, and entitled “Dual Stage Ion Exchange for Chemical Strengtheningof Glass,” and claiming priority from U.S. Provisional PatentApplication No. 61/084,398, filed Jul. 29, 2008, in which glasssubstrates are strengthened by ion exchange in a first bath is dilutedwith an effluent ion, followed by immersion in a second bath having asmaller concentration of the effluent ion than the first bath. Thecontents of U.S. patent application Ser. No. 12/500,650 and U.S. Pat.No. 8,312,739 are incorporated herein by reference in their entirety.

The degree of chemical strengthening achieved by ion exchange may bequantified based on the parameters of central tension (CT), surface CS,and depth of layer (DOL). Surface CS may be measured near the surface orwithin the strengthened glass at various depths. A maximum CS value mayinclude the measured CS at the surface (CS_(s)) of the strengthenedsubstrate. The CT, which is computed for the inner region adjacent thecompressive stress layer within a glass substrate, can be calculatedfrom the CS, the physical thickness t, and the DOL. CS and DOL aremeasured using those means known in the art. Such means include, but arenot limited to, measurement of surface stress (FSM) using commerciallyavailable instruments such as the FSM-6000, manufactured by Luceo Co.,Ltd. (Tokyo, Japan), or the like, and methods of measuring CS and DOLare described in ASTM 1422C-99, entitled “Standard Specification forChemically Strengthened Flat Glass,” and ASTM 1279.19779 “Standard TestMethod for Non-Destructive Photoelastic Measurement of Edge and SurfaceStresses in Annealed, Heat-Strengthened, and Fully-Tempered Flat Glass,”the contents of which are incorporated herein by reference in theirentirety. Surface stress measurements rely upon the accurate measurementof the stress optical coefficient (SOC), which is related to thebirefringence of the glass substrate. SOC in turn is measured by thosemethods that are known in the art, such as fiber and four point bendmethods, both of which are described in ASTM standard C770-98 (2008),entitled “Standard Test Method for Measurement of Glass Stress-OpticalCoefficient,” the contents of which are incorporated herein by referencein their entirety, and a bulk cylinder method. The relationship betweenCS and CT is given by the expression (1):

CT=(CS·DOL)/(t−2 DOL)  (1),

wherein t is the physical thickness (μm) of the glass article. Invarious sections of the disclosure, CT and CS are expressed herein inmegaPascals (MPa), physical thickness t is expressed in eithermicrometers (μm) or millimeters (mm) and DOL is expressed in micrometers(μm).

In one embodiment, a strengthened substrate 110 can have a surface CS of250 MPa or greater, 300 MPa or greater, e.g., 400 MPa or greater, 450MPa or greater, 500 MPa or greater, 550 MPa or greater, 600 MPa orgreater, 650 MPa or greater, 700 MPa or greater, 750 MPa or greater or800 MPa or greater. The strengthened substrate may have a DOL of 10 μmor greater, 15 μm or greater, 20 μm or greater (e.g., 25 μm, 30 μm, 35μm, 40 μm, 45 μm, 50 μm or greater) and/or a CT of 10 MPa or greater, 20MPa or greater, 30 MPa or greater, 40 MPa or greater (e.g., 42 MPa, 45MPa, or 50 MPa or greater) but less than 100 MPa (e.g., 95, 90, 85, 80,75, 70, 65, 60, 55 MPa or less). In one or more specific embodiments,the strengthened substrate has one or more of the following: a surfaceCS greater than 500 MPa, a DOL greater than 15 μm, and a CT greater than18 MPa.

Example glasses that may be used in the substrate may include alkalialuminosilicate glass compositions or alkali aluminoborosilicate glasscompositions, though other glass compositions are contemplated. Suchglass compositions are capable of being chemically strengthened by anion exchange process. One example glass composition comprises SiO₂, B₂O₃and Na₂O, where (SiO₂+B₂O₃)≧66 mol. %, and Na₂O≧9 mol. %.

In an embodiment, the glass composition includes at least 6 wt. %aluminum oxide. In a further embodiment, the substrate includes a glasscomposition with one or more alkaline earth oxides, such that a contentof alkaline earth oxides is at least 5 wt. %. Suitable glasscompositions, in some embodiments, further comprise at least one of K₂O,MgO, and CaO. In a particular embodiment, the glass compositions used inthe substrate can comprise 61-75 mol. % SiO2; 7-15 mol. % Al₂O₃; 0-12mol. % B₂O₃; 9-21 mol. % Na₂O; 0-4 mol. % K₂O; 0-7 mol. % MgO; and 0-3mol. % CaO.

A further example glass composition suitable for the substratecomprises: 60-70 mol. % SiO₂; 6-14 mol. % Al₂O₃; 0-15 mol. % B₂O₃; 0-15mol. % Li₂O; 0-20 mol. % Na₂O; 0-10 mol. % K₂O; 0-8 mol. % MgO; 0-10mol. % CaO; 0-5 mol. % ZrO₂; 0-1 mol. % SnO₂; 0-1 mol. % CeO₂; less than50 ppm As₂O₃; and less than 50 ppm Sb₂O₃; where 12 mol.%≦(Li₂O+Na₂O+K₂O)≦20 mol. % and 0 mol. %≦(MgO+CaO)≦10 mol. %.

A still further example glass composition suitable for the substratecomprises: 63.5-66.5 mol. % SiO₂; 8-12 mol. % Al₂O₃; 0-3 mol. % B₂O₃;0-5 mol. % Li₂O; 8-18 mol. % Na₂O; 0-5 mol. % K₂O; 1-7 mol. % MgO; 0-2.5mol. % CaO; 0-3 mol. % ZrO₂; 0.05-0.25 mol. % SnO₂; 0.05-0.5 mol. %CeO₂; less than 50 ppm As₂O₃; and less than 50 ppm Sb₂O₃; where 14 mol.%≦(Li₂O+Na₂O+K₂O)≦18 mol. % and 2 mol. %≦(MgO+CaO)≦7 mol. %.

In a particular embodiment, an alkali aluminosilicate glass compositionsuitable for the substrate comprises alumina, at least one alkali metaland, in some embodiments, greater than 50 mol. % SiO₂, in otherembodiments at least 58 mol. % SiO₂, and in still other embodiments atleast 60 mol. % SiO₂, wherein the ratio (Al₂O₃+B₂O₃)/Σmodifiers (i.e.,sum of modifiers) is greater than 1, where in the ratio the componentsare expressed in mol. % and the modifiers are alkali metal oxides. Thisglass composition, in particular embodiments, comprises: 58-72 mol. %SiO₂; 9-17 mol. % Al₂O₃; 2-12 mol. % B₂O₃; 8-16 mol. % Na₂O; and 0-4mol. % K₂O, wherein the ratio (Al₂O₃+B₂O₃)/Σmodifiers (i.e., sum ofmodifiers) is greater than 1.

In still another embodiment, the substrate may include an alkalialuminosilicate glass composition comprising: 64-68 mol. % SiO₂; 12-16mol. % Na₂O; 8-12 mol. % Al₂O₃; 0-3 mol. % B₂O₃; 2-5 mol. % K₂O; 4-6mol. % MgO; and 0-5 mol. % CaO, wherein: 66 mol. %≦SiO₂+B₂O₃+CaO≦69 mol.%; Na₂O+K₂O+B₂O₃+MgO+CaO+SrO>10 mol. %; 5 mol. %≦MgO+CaO+SrO≦8 mol. %;(Na₂O+B₂O₃)—Al₂O₃≦2 mol. %; 2 mol. %≦Na₂O—Al₂O₃≦6 mol. %; and 4 mol.%≦(Na₂O+K₂O)−Al₂O₃≦10 mol. %.

In an alternative embodiment, the substrate may comprise an alkalialuminosilicate glass composition comprising: 2 mol % or more of Al₂O₃and/or ZrO₂, or 4 mol % or more of Al₂O₃ and/or ZrO₂.

Where the substrate 110 includes a crystalline substrate, the substratemay include a single crystal, which may include Al₂O₃. Such singlecrystal substrates are referred to as sapphire. Other suitable materialsfor a crystalline substrate include polycrystalline alumina layer and/orspinel (MgAl₂O₄).

Optionally, the crystalline substrate 110 may include a glass ceramicsubstrate, which may be strengthened or non-strengthened. Examples ofsuitable glass ceramics may include Li₂O—Al₂O₃—SiO₂ system (i.e.LAS-System) glass ceramics, MgO—Al₂O₃—SiO₂ system (i.e. MAS-System)glass ceramics, and/or glass ceramics that include a predominant crystalphase including β-quartz solid solution, β-spodumene ss, cordierite, andlithium disilicate. The glass ceramic substrates may be strengthenedusing the chemical strengthening processes disclosed herein. In one ormore embodiments, MAS-System glass ceramic substrates may bestrengthened in Li₂SO₄ molten salt, whereby an exchange of 2Li⁺ for Mg⁺can occur.

The substrate 110 according to one or more embodiments can have aphysical thickness ranging from about 100 μm to about 5 mm. Examplesubstrate 110 physical thicknesses range from about 100 μm to about 500μm (e.g., 100, 200, 300, 400 or 500 μm). Further example substrate 110physical thicknesses range from about 500 μm to about 1000 μm (e.g.,500, 600, 700, 800, 900 or 1000 μm). The substrate 110 may have aphysical thickness greater than about 1 mm (e.g., about 2, 3, 4, or 5mm) In one or more specific embodiments, the substrate 110 may have aphysical thickness of 2 mm or less or less than 1 mm. The substrate 110may be acid polished or otherwise treated to remove or reduce the effectof surface flaws.

Anti-Reflective Coating

As shown in FIG. 1, the anti-reflective coating 130 may include aplurality of layers such that one or more layers may be disposed on theopposite side of the substrate 110 from the anti-reflective coating 130(i.e., on major surface 114)(shown in FIG. 1).

The physical thickness of the anti-reflective coating 130 disposed onthe major surface 114 may be in the range from about 0.1 μm to about 5μm. In some instances, the physical thickness of the anti-reflectivecoating 140 disposed on major surface 114 may be in the range from about0.01 μm to about 0.9 μm, from about 0.01 μm to about 0.8 μm, from about0.01 μm to about 0.7 μm, from about 0.01 μm to about 0.6 μm, from about0.01 μm to about 0.5 μm, from about 0.01 μm to about 0.4 μm, from about0.01 μm to about 0.3 μm, from about 0.01 μm to about 0.2 μm, from about0.01 μm to about 0.1 μm, from about 0.02 μm to about 1 μm, from about0.03 μm to about 1 μm, from about 0.04 μm to about 1 μm, from about 0.05μm to about 1 μm, from about 0.06 μm to about 1 μm, from about 0.07 μmto about 1 μm, from about 0.08 μm to about 1 μm, from about 0.09 μm toabout 1 μm, from about 0.2 μm to about 1 μm, from about 0.3 μm to about5 μm, from about 0.4 μm to about 3 nm, from about 0.5 μm to about 3 μm,from about 0.6 μm to about 2 μm, from about 0.7 μm to about 1 μm, fromabout 0.8 μm to about 1 μm, or from about 0.9 μm to about 1 μm, and allranges and sub-ranges therebetween.

Exemplary embodiments of the articles described herein are providedbelow in Tables 1-2.

TABLE 1 Exemplary articles including 12-layer optical coating. Example AExample B Example C Physical Physical Physical Refractive ThicknessRefractive Thickness Refractive Thickness Layer Material Index (nm)Index (nm) Index (nm) Medium Air 1 1 1 12 SiO2 1.46929 91.46 1.4692983.02 1.43105 79.41 11 AlO_(x)N_(y) 1.97879 154.26 1.97879 152.941.97879 159.84 10 SiO2 1.46929 21.74 1.46929 27.14 1.43105 26.53 9AlO_(x)N_(y) 1.97879 51.85 1.97879 49.8 1.97879 51.67 8 SiO2 1.4692914.03 1.46929 17.12 1.43105 15.47 7 AlO_(x)N_(y) 1.97879 2000 1.978792000 1.97879 2000 6 SiO2 1.46929 8.51 1.46929 8.51 1.43105 8.13 5AlO_(x)N_(y) 1.97879 43.16 1.97879 43.16 1.97879 45.34 4 SiO2 1.4692928.82 1.46929 28.82 1.43105 27.69 3 AlO_(x)N_(y) 1.97879 25.49 1.9787925.49 1.97879 28.38 2 SiO2 1.46929 49.24 1.46929 49.24 1.43105 45.85 1AlO_(x)N_(y) 1.97879 8.49 1.97879 8.49 1.97879 10.14 Substrate Glass1.50542 1.50542 1.50542 Total Optical Coating Thickness 2497.06 2493.732498.44 Example D Example E Example F Physical Physical PhysicalRefractive Thickness Refractive Thickness Refractive Thickness LayerMaterial Index (nm) Index (nm) Index (nm) Medium Air 1 1 1 12 SiO21.48114 95.18 1.48114 86.3 1.48114 81.55 11 AlO_(x)N_(y) 2.00605 154.992.00605 149.05 2.00605 150.12 10 SiO2 1.48114 23.23 1.48114 25.061.48114 27.61 9 AlO_(x)N_(y) 2.00605 50.7 2.00605 48.53 2.00605 47.69 8SiO2 1.48114 14.82 1.48114 16 1.48114 17.43 7 AlO_(x)N_(y) 2.00605 20002.00605 2000 2.00605 2000 6 SiO2 1.48114 8.7 1.48114 8.7 1.48114 8.7 5AlO_(x)N_(y) 2.00605 43.17 2.00605 43.17 2.00605 43.17 4 SiO2 1.4811429.77 1.48114 29.77 1.48114 29.77 3 AlO_(x)N_(y) 2.00605 24.96 2.0060524.96 2.00605 24.96 2 SiO2 1.48114 52.22 1.48114 52.22 1.48114 52.22 1AlO_(x)N_(y) 2.00605 8.01 2.00605 8.01 2.00605 8.01 Substrate Glass1.50542 1.50542 1.50542 Total Optical Coating Thickness 2505.75 2491.772491.23 Example G Example H Example I Physical Physical PhysicalRefractive Thickness Refractive Thickness Refractive Thickness LayerMaterial Index (nm) Index (nm) Index (nm) Medium Air 1 1 1 12 SiO21.48962 82.74 1.46929 85.06 1.49675 84.37 11 AlO_(x)N_(y) 2.07891 144.971.97879 150.86 2.06723 144.46 10 SiO2 1.48962 26.43 1.46929 26.541.49675 25.92 9 AlO_(x)N_(y) 2.07891 46.45 1.97879 48.63 2.06723 46.59 8SiO2 1.48962 17.08 1.46929 16.86 1.49675 16.56 7 AlO_(x)N_(y) 2.078912000 1.97879 2000 2.06723 2000 6 SiO2 1.48962 8.73 1.46929 8.56 1.496758.72 5 AlO_(x)N_(y) 2.07891 41.35 1.97879 44.1 2.06723 41.51 4 SiO21.48962 29.94 1.46929 29.35 1.49675 30.05 3 AlO_(x)N_(y) 2.07891 23.51.97879 25.95 2.06723 23.42 2 SiO2 1.48962 52.68 1.46929 50.28 1.4967553.7 1 AlO_(x)N_(y) 2.07891 7.36 1.97879 8.55 2.06723 7.21 SubstrateGlass 1.511 1.50542 1.50542 Total Optical Coating Thickness 2481.222494.75 2482.51

TABLE 2 Article including 16-layer optical coating. Example J Example KExample L Physical Physical Physical Refractive Thickness RefractiveThickness Refractive Thickness Layer Material Index (nm) Index (nm)Index (nm) Medium Air 1 1 1 16 SiO2 1.46929 91.07 1.46929 91.28 1.4707988.31 15 AlO_(x)N_(y) 1.97879 163.1 1.97879 163.28 1.95183 157.24 14SiO2 1.46929 9.33 1.46929 9.01 1.47079 7.14 13 AlO_(x)N_(y) 1.97879 96.41.97879 97.14 1.95183 108.17 12 SiO2 1.46929 24.03 1.46929 23.95 1.4707927.86 11 AlO_(x)N_(y) 1.97879 41.3 1.97879 41.26 1.95183 31.47 10 SiO21.46929 47.23 1.46929 46.9 1.47079 63.22 9 AlO_(x)N_(y) 1.97879 38.691.97879 38.64 1.95183 30.41 8 SiO2 1.46929 20.25 1.46929 20.35 1.4707927.81 7 AlO_(x)N_(y) 1.97879 2000 1.97879 2000 1.95183 2000 6 SiO21.46929 8.56 1.46929 8.56 1.47079 8.39 5 AlO_(x)N_(y) 1.97879 44.11.97879 44.1 1.95183 45.24 4 SiO2 1.46929 29.35 1.46929 29.35 1.4707928.73 3 AlO_(x)N_(y) 1.97879 25.95 1.97879 25.95 1.95183 27.21 2 SiO21.46929 50.28 1.46929 50.28 1.47079 48.4 1 AlO_(x)N_(y) 1.97879 8.551.97879 8.55 1.95183 9.21 Substrate Glass 1.50542 1.50542 1.50996 TotalOptical Coating Thickness 2698.2 2698.6 2708.79 Example M Example NExample O Physical Physical Physical Refractive Thickness RefractiveThickness Refractive Thickness Layer Material Index (nm) Index (nm)Index (nm) Medium Air 1 1 1 16 SiO2 1.47079 92.73 1.47503 93.15 1.4811488.58 15 AlO_(x)N_(y) 1.95183 156.68 1.98174 162.83 2.00605 158.86 14SiO2 1.47079 7.3 1.47503 15.52 1.48114 10.2 13 AlO_(x)N_(y) 1.95183102.39 1.98174 74.88 2.00605 95.49 12 SiO2 1.47079 27.78 1.47503 16.041.48114 20.08 11 AlO_(x)N_(y) 1.95183 30.01 1.98174 60.83 2.00605 44.7910 SiO2 1.47079 64.5 1.47503 23.28 1.48114 41.36 9 AlO_(x)N_(y) 1.9518327.42 1.98174 49.82 2.00605 40.02 8 SiO2 1.47079 29.06 1.47503 12.21.48114 19.18 7 AlO_(x)N_(y) 1.95183 2000 1.98174 2000 2.00353 2000 6SiO2 1.47079 8.39 1.47503 8.3 1.48114 8.79 5 AlO_(x)N_(y) 1.95183 45.241.98174 46.8 2.00605 42.85 4 SiO2 1.47079 28.73 1.47503 29.1 1.4811429.89 3 AlO_(x)N_(y) 1.95183 27.21 1.98174 27.4 2.00605 24.91 2 SiO21.47079 48.4 1.47503 51.3 1.48114 52.29 1 AlO_(x)N_(y) 1.95183 9.211.98174 9.4 2.00605 8 Substrate Glass 1.50996 1.511 1.50542 TotalOptical Coating Thickness 2705.05 2680.86 2685.29 Example P Example QExample R Physical Physical Physical Refractive Thickness RefractiveThickness Refractive Thickness Layer Material Index (nm) Index (nm)Index (nm) Medium Air 1 1 1 16 SiO2 1.46774 89.81 1.47172 92.97 1.495289.3 15 AlO_(x)N_(y) 2.04423 148.85 2.05892 149.36 2.08734 150.63 14SiO2 1.46774 27.95 1.47172 25.6 1.4952 9.14 13 AlO_(x)N_(y) 2.0442353.42 2.05892 52.83 2.08734 98.24 12 SiO2 1.46774 39.06 1.47172 38.261.4952 19.24 11 AlO_(x)N_(y) 2.04423 40.17 2.05892 39.2 2.08734 40.7 10SiO2 1.46774 54.76 1.47172 51.09 1.4952 39.66 9 AlO_(x)N_(y) 2.0442335.8 2.05892 36.17 2.08734 37.3 8 SiO2 1.46774 26.97 1.47172 24.751.4952 17.82 7 AlO_(x)N_(y) 2.04423 2000 2.05892 2000 2.08734 2000 6SiO2 1.46774 8.51 1.47172 8.51 1.4952 8.72 5 AlO_(x)N_(y) 2.04423 42.252.05892 42.25 2.08734 41.04 4 SiO2 1.46774 29.16 1.47172 29.16 1.495229.92 3 AlO_(x)N_(y) 2.04423 24.84 2.05892 24.84 2.08734 23.26 2 SiO21.46774 50.45 1.47172 50.45 1.4952 53.63 1 AlO_(x)N_(y) 2.04423 8.192.05892 8.19 2.08734 7.22 Substrate Glass 1.50996 1.50996 1.50996 TotalOptical Coating Thickness 2680.2 2673.64 2665.82 Example S PhysicalRefractive Thickness Layer Material Index (nm) Medium Air 1 16 SiO21.4952 92.38 15 AlO_(x)N_(y) 2.08734 150.06 14 SiO2 1.4952 10.05 13AlO_(x)N_(y) 2.08734 96.93 12 SiO2 1.4952 18.89 11 AlO_(x)N_(y) 2.0873441.87 10 SiO2 1.4952 40.14 9 AlO_(x)N_(y) 2.08734 37.64 8 SiO2 1.495217.38 7 AlO_(x)N_(y) 2.08734 2000 6 SiO2 1.4952 8.72 5 AlO_(x)N_(y)2.08734 41.04 4 SiO2 1.4952 29.92 3 AlO_(x)N_(y) 2.08734 23.26 2 SiO21.4952 53.63 1 AlO_(x)N_(y) 2.08734 7.22 Substrate Glass 1.50996 TotalThickness 2669.12

As shown in Tables 1 and 2, the physical thickness of the layers of theoptical film may vary, with the scratch resistant layer (layer 6) havingthe greatest thickness. The physical thickness ranges for the layers maybe as shown in Tables 3-4. In both the 16-layer and 12-layer designsabove, layer 7 has the greatest physical thickness and impartssignificant hardness and scratch resistance to the optical coating andthe article. It should be understood that a different layer could bemade to have the greatest physical thickness. However, in theseparticular designs, the impedance matching layers above and below thethickest layer (in this case, layer 7) mean that there is a largeoptical design freedom for adjusting the thickness of the thickestlayer, as shown in Tables 3-4 below.

TABLE 3 Layer thickness range for exemplary 12-layer optical coating.layer min max 12 60 120 11 120 180 10 20 30 9 40 55 8 10 20 7 150 5000 65 15 5 35 50 4 25 35 3 20 30 2 40 60 1 5 12

TABLE 4 Layer thickness range for exemplary 16-layer optical coatings.layer min max 16 60 120 15 120 180 14 5 35 13 40 110 12 10 45 11 25 7010 20 70 9 20 60 8 5 40 7 150 5000 6 5 15 5 30 50 4 20 40 3 20 40 2 3060 1 5 15

A second aspect of this disclosure pertains to a method for forming thearticles described herein. In one embodiment, the method includesproviding a substrate having a major surface in a coating chamber,forming a vacuum in the coating chamber, forming a durable opticalcoating as described herein on the major surface, optionally forming anadditional coating comprising at least one of an easy-to-clean coatingand a scratch resistant coating, on the optical coating, and removingthe substrate from the coating chamber. In one or more embodiments, theoptical coating and the additional coating are formed in either the samecoating chamber or without breaking vacuum in separate coating chambers.

In one or more embodiments, the method may include loading the substrateon carriers which are then used to move the substrate in and out ofdifferent coating chambers, under load lock conditions so that a vacuumis preserved as the substrate is moved.

The optical coating 120 and/or the additional coating 140 may be formedusing various deposition methods such as vacuum deposition techniques,for example, chemical vapor deposition (e.g., plasma enhanced chemicalvapor deposition (PECVD), low-pressure chemical vapor deposition,atmospheric pressure chemical vapor deposition, and plasma-enhancedatmospheric pressure chemical vapor deposition), physical vapordeposition (e.g., reactive or nonreactive sputtering or laser ablation),thermal or e-beam evaporation and/or atomic layer deposition.Liquid-based methods may also be used such as spraying, dipping, spincoating, or slot coating (for example, using sol-gel materials). Wherevacuum deposition is utilized, inline processes may be used to form theoptical coating 120 and/or the additional coating 140 in one depositionrun. In some instances, the vacuum deposition can be made by a linearPECVD source.

In some embodiments, the method may include controlling the thickness ofthe optical coating 120 and/or the additional coating 140 so that itdoes not vary by more than about 4% along at least about 80% of the areaof the anti-reflective surface 122 or from the target thickness for eachlayer at any point along the substrate area. In some embodiments, thethickness of the optical coating 120 and/or the additional coating 140so that it does not vary by more than about 4% along at least about 95%of the area of the anti-reflective surface 122.

EXAMPLES

Various embodiments will be further clarified by the following examples.In the Examples, it should be noted that AlOxNy and SiuAlvOxNy werefound to be substantially interchangeable as the high-index material inthe modeled examples, with only minor process adjustments necessary tore-create the targeted refractive index dispersion values and layerthickness designs provided, which are apparent to one of ordinary skillin the art.

Example 1

Example 1 included a 12-layer optical coating 300, including layers 305,310, 320, 330, 340, 350, 360, 370, 380, 390 and 400 sequentiallydisposed on top of one another, and disposed on a strengthenedaluminosilicate glass substrate 201 having a nominal composition ofabout 58 mol % SiO₂, 16.5 mol % Al₂O₃, 17 mol % Na₂O, 3 mol % MgO, andabout 6.5 mol % P₂O₅. The optical coating 300 also includes a scratchresistant layer 345 (including sub-layers 345A-345I) disposed within thelayers of the anti-reflective coating. The structure of the article isshown in FIG. 8 (the thicknesses shown in FIG. 8 are not exact andintended to be illustrative) and the relative thicknesses of the layersare shown in Table 5.

Both SiO₂ and Si_(x)Al_(v)O_(x)N_(y) layers were made by reactivesputtering in an AJA-Industries Sputter Deposition Tool. SiO₂ wasdeposited by DC reactive sputtering from an Si target with ion assist;Si_(u)Al_(v)O_(x)N_(y) material was deposited by DC reactive sputteringcombined with RF superimposed DC sputtering with ion assist. The targetswere 3″ diameter Silicon and 3″ diameter Al. The reactive gasses werenitrogen and oxygen, and the “working” (or inert) gas was Argon. Thepower supplied to the Silicon was radio frequency (RF) at 13.56 Mhz. Thepower supplied to the Aluminum was DC.

The sputtering process conditions by which the structure of theanti-reflective coating were made are shown in Table 6.

Layers 340 and 345A-I of period 3 included a layer having asubstantially homogenous composition (layer 340) and plurality oflayers, when compared to one another, having a refractive index gradient(layers 345A-345I) formed from altering the composition of the pluralityof layers from one layer to the next adjacent layer so the refractiveindex increases step-wise or monotonically from 2.015 to 2.079 to 2.015,as shown in Table 5. The refractive indices of layers 345B-D and 345F-Hwere not measured but were estimated based on known methods in the art.The article fabricated according to Example 1 exhibited significantlyimproved abrasion resistance compared to the abrasion and scratchresistance of a comparative uncoated bare glass substrate together withreflectance below 1% over a portion of the optical wavelength regime.

TABLE 5 Structure of Example 1. Refractive Target Index Physical LayerPeriods Material @ 550 nm Thickness Ambient — Air 1 medium Optical 1SiO₂ (305) 1.483 87.84 nm coating Si_(u)Al_(v)O_(x)N_(y) (310) 2.015147.92 nm  2 SiO₂ (320) 1.483 20.32 nm Si_(u)Al_(v)O_(x)N_(y) (330)2.015 49.63 nm 3 SiO₂ (340) 1.483 11.86 nm Si_(u)Al_(v)O_(x)N_(y) (345A)2.015 84.11 nm Si_(u)Al_(v)O_(x)N_(y) (345B) 2.031* 88.54 nmSi_(u)Al_(v)O_(x)N_(y) (345C) 2.047* 92.98 nm Si_(u)Al_(v)O_(x)N_(y)(345D) 2.063* 97.41 nm Si_(u)Al_(v)O_(x)N_(y) (345E) 2.079 1219.51 nm Si_(u)Al_(v)O_(x)N_(y) (345F) 2.063* 97.41 nm Si_(u)Al_(v)O_(x)N_(y)(345G) 2.047* 92.98 nm Si_(u)Al_(v)O_(x)N_(y) (345H) 2.031* 88.54 nmSi_(u)Al_(v)O_(x)N_(y) (345I) 2.015 84.11 nm 4 SiO₂ (350) 1.483  8.38 nmSi_(u)Al_(v)O_(x)N_(y) (360) 2.015 45.98 nm 5 SiO₂ (370) 1.483 33.21 nmSi_(u)Al_(v)O_(x)N_(y) (380) 2.015 24.96 nm 6 SiO₂ (390) 1.483 60.17 nmSi_(u)Al_(v)O_(x)N_(y) (392) 2.015  8.78 nm Substrate — AS Glass(500) 1. 51005 — Total Coating Thickness 2444.64 nm 

TABLE 6 DC/RF Reactive Sputtering Process Conditions for Example 1. ArFlow N2 flow O2 flow Al Al Si P Layer(s) (sccm) (sccm) (sccm) Wrf WdcWrf (torr) 305, 320, 30 30 3.3 75 50 500 4 340, 350, 370, 390 310, 330,30 30 0.5 200 300 500 4 360, 780, 392 345A, 345I 30 30 0.5 200 300 500 4345B, 345H 30 30 0.5 200 300 500 3.5 345C, 345G 30 30 0.5 200 300 500 3345D, 345F 30 30 0.5 200 300 500 2.5 345E 30 30 0.5 200 300 500 2

Modeled Examples 2-3 & Comparative Modeled Example 4

Modeled Examples 2-3 used modeling to demonstrate the reflectancespectra of articles that included embodiments of the optical coating, asdescribed herein. In Modeled Examples 2-5, the optical coating includedSi_(u)Al_(v)O_(x)N_(y) and SiO₂ layers, and a strengthenedaluminosilicate glass substrate having a nominal composition of about 58mol % SiO₂, 17 mol % Al₂O₃, 17 mol % Na₂O, 3 mol % MgO, 0.1 mol % SnO,and 6.5 mol % P₂O₅.

To determine the refractive index dispersion curves for the coatingmaterials, layers of each coating material were formed onto siliconwafers by DC, RF or RF superimposed DC reactive sputtering from asilicon, aluminum, silicon and aluminum combined or co-sputtered, ormagnesium fluoride target (respectively) at a temperature of about 50°C. using ion assist. The wafer was heated to 200° C. during depositionof some layers and targets having a 3 inch diameter were used. Reactivegases used included nitrogen, fluorine and oxygen; argon was used as theinert gas. The RF power was supplied to the silicon target at 13.56 Mhzand DC power was supplied to the Si target, Al target and other targets.

The refractive indices (as a function of wavelength) of each of theformed layers and the glass substrate were measured using spectroscopicellipsometry. The refractive indices thus measured were then used tocalculate reflectance spectra for Modeled Examples 2-5. The modeledexamples use a single refractive index value in their descriptive tablesfor convenience, which corresponds to a point selected from thedispersion curves at about 550 nm wavelength.

Modeled Example 2 included a 12-layer optical coating with layerssequentially disposed on top of one another, disposed on a strengthenedaluminosilicate glass substrate 200, as shown in Table 7.

TABLE 7 Structure of Modeled Example 2. Refractive Index @ ModeledPhysical Layer Periods Material 550 nm Thickness Ambient — Air 1 mediumoptical 1 SiO₂-a 1.4826 87 nm reflective Si_(u)Al_(v)O_(x)N_(y) 2.015149 nm coating 2 SiO₂-a 1.4826 20 nm Si_(u)Al_(v)O_(x)N_(y) 2.015 50 nmSiO₂-a 1.4826 12 nm Scratch Si_(u)Al_(v)O_(x)N_(y) 2.015 505 nm (butvariable resistant in the range from about layer 100 nm to about 5000nm) 3 SiO₂-a 1.4826 9 nm Si_(u)Al_(v)O_(x)N_(y) 2.015 48 nm 4 SiO₂-a1.4826 33 nm Si_(u)Al_(v)O_(x)N_(y) 2.015 25 nm 5 SiO₂-a 1.4826 60 nmSi_(u)Al_(v)O_(x)N_(y) 2.015 8 nm Substrate — AS Glass 1.51005

The reflectance of a single side of the article of Modeled Example 2 wascalculated at different viewing incident illumination angles or angle ofillumination (“AOI”) and the resulting reflectance spectra is shown inFIG. 9. The reflected color, based on a 10° observer under a D65illuminant and a F2 illuminant was also measured and the a* and b*values are plotted as the incident illumination angle or AOI changedfrom 0 degrees to about 60 degrees from normal incidence at regularincrements. The plot showing the reflected color is shown in FIG. 10.

Modeled Example 3 included a 10-layer optical coating with layerssequentially disposed on top of one another, disposed on a strengthenedaluminosilicate glass substrate 200. The relative thicknesses of thelayers are shown in Table 8.

TABLE 18 Structure of Modeled Example 3. Refractive Modeled Index @Physical Layer Periods Material 550 nm Thickness Ambient — Air 1 mediumOptical 1 SiO₂-a 1.4826 79 nm coating Si_(u)Al_(v)O_(x)N_(y) 2.015 170nm SiO₂-a 1.4826 12 nm Scratch Si_(u)Al_(v)O_(x)N_(y) 2.015 350 nm (butResistant variable in layer the range from about 100 nm to about 2000nm) 2 SiO₂-a 1.4826 6 nm Si_(u)Al_(v)O_(x)N_(y) 2.015 69 nm 3 SiO₂-a1.4826 18 nm Si_(u)Al_(v)O_(x)N_(y) 2.015 20 nm 4 SiO₂-a 1.4826 23 nmSi_(u)Al_(v)O_(x)N_(y) 2.015 15 nm Substrate — AS Glass 1.51005

The reflectance of a single side of the article of Modeled Example 3 wascalculated at different viewing incident illumination angles or angle ofillumination (“AOI”) and the resulting reflectance spectra is shown inFIG. 11. The reflected color, based on a 10° observer under a D65illuminant and a F2 illuminant was also measured and the a* and b*values are plotted as the incident illumination angle or AOI changedfrom 0 degrees to about 60 degrees from normal incidence at regularincrements. The plot showing the reflected color is shown in FIG. 12.

The optical performance of Modeled Examples 3 was compared toComparative Modeled Example 4, which included a 6-layer anti-reflectivecoating of alternating Nb₂O₅ and SiO₂ layers and a hydrophobic coatingdisposed on the anti-reflective coating. To generate Comparative ModeledExample 4, ion-assisted e-beam deposition was used to deposit a singlelayer of Nb₂O₅ onto a silicon wafer and a single layer of SiO₂ onto asilicon wafer. The refractive indices as a function of wavelength forthese layers were measured using spectroscopic ellipsometry. Themeasured refractive indices were then used in Comparative ModeledExample 4. The optical performance evaluated includes averagereflectance over the wavelength range from about 450 nm to about 650 nmand color shift (with reference to a* and b* coordinates (−1, −1), usingthe equation √((a*_(example)−(−1))²+(b*_(example)−(−1))²)) when viewedat an incident illumination angles in the range from about 0 degrees toabout 60 degrees from normal incidence under F02 and D65 illuminants.Table 9 shows the average reflectance and the greatest color shift ofModeled Example 3, and Comparative Modeled Example 4.

TABLE 9 Average Reflectance and Color Shift for Modeled Example 3andComparative Modeled Example 4. Avg. Color Shift Reflectance Referencedto Ex. 450-650 nm (%) (a*, b*) = (−1, −1) Modeled Example 3, 10-layer1.5 1.5 Si_(u)Al_(v)O_(x)N_(y) or AlO_(x)N_(y)/SiO₂ Modeled Comp. Ex. 4,6-layer 0.3 7.9 Nb2O5/SiO₂/hydrophobic coating

As shown in Table 12, while Comparative Modeled 4 exhibited a loweraverage reflectance, it also exhibited the greatest color shift. ModeledExample 3 had significantly less color shift though, althoughreflectance was increased slightly. Based on fabrication and testing ofsimilar coatings with similar materials, it is believed that ModeledExample 3 would have exhibited superior scratch and abrasion resistanceover Comparative Modeled Example 4.

Example 5

Example 5 included a strengthened aluminosilicate glass substrate havinga nominal composition of about 58 mol % SiO₂, 17 mol % Al₂O₃, 17 mol %Na₂O, 3 mol % MgO, 0.1 mol % SnO, and 6.5 mol % P₂O₅ and a 16-layeroptical coating including a 2 micrometer scratch resistant layer, asshow in Table 10.

TABLE 10 Structure of Example 5. Refractive Physical Periods, if IndexThickness Coating/Layer applicable Material (@ 550 nm) (nm) Ambient —Air medium Optical 1 SiO₂ 1.47503 92.6 coating AlO_(x)N_(y) 1.98174163.8 2 SiO₂ 1.47503 15.7 AlO_(x)N_(y) 1.98174 72.3 3 SiO₂ 1.47503 16.5AlO_(x)N_(y) 1.98174 62.9 4 SiO₂ 1.47503 22.5 AlO_(x)N_(y) 1.98174 53.2SiO₂ 1.47503 12.5 Scratch- AlO_(x)N_(y) 1.98174 2000 Resistant Layer 5SiO₂ 1.47503 8.3 AlO_(x)N_(y) 1.98174 46.8 6 SiO₂ 1.47503 29.1AlO_(x)N_(y) 1.98174 27.4 7 SiO₂ 1.47503 51.3 AlO_(x)N_(y) 1.98174 9.4 —— AS Glass 1.51005 Total coating thickness 2684.3

Example 5 exhibited a single side photopic average reflectance (i.e.,measured from the anti-reflective surface 122) over the opticalwavelength regime under D65 illumination at incident illumination anglesof 0 °, 30°, 45° and 60°, of 0.71%, 0.76%, 1.43%, and 4.83%,respectively. Example 5 exhibited a single side photopic averagetransmittance (i.e., measured through the anti-reflective surface 122)over the optical wavelength regime under D65 illumination at incidentillumination angles of 0 °, 30 °, 45° and 60°, of 99.26%, 99.21%,98.54%, and 95.14%, respectively.

Example 5 exhibited a total photopic average reflectance (i.e., measuredfrom the anti-reflective surface 122 and the opposite major surface 114)over the optical wavelength regime under D65 illumination at incidentillumination angles of 0 °, 30°, 45° and 60°, of 4.80%, 4.99%, 6.36%,and 12.64%, respectively. Example 5 exhibited a total photopic averagetransmittance (i.e., measured through the anti-reflective surface 122and the opposite major surface 114) over the optical wavelength regimeunder D65 illumination at incident illumination angles of 0 °, 30 °, 45°and 60°, of 95.18%, 94.99%, 93.61%, and 87.33%, respectively.

The reflectance and transmitted color coordinates for a single surface(i.e., anti-reflective surface 122) and two surfaces (i.e.,anti-reflective surface 122 and major surface 114, of FIG. 1) of Example5, under incident illumination angles or AOI from 0 degrees to 60degrees and illuminants D65 and F2 are shown in Tables 11A-11D. Singlesurface color coordinates were measured by eliminating transmission orreflectance from the major surface 114, as is known in the art. Thecolor shift is calculated using the following equation:√((a*₂−a*₁)²+(b*₂−b*₁)²), with a*₁, and b*₁ representing the a* and b*coordinates of the article when viewed at normal incidence (i.e., AOI=0)and a*₂, and b*₂ representing the a* and b* coordinates of the articlewhen viewed at an incident illumination angle different or away fromnormal incidence (i.e., AOI=1-60).

TABLE 11A One surface reflectance and transmitted color coordinates (Y,L*, a* and b*) using illuminant D65 for Example 5. Reflectance, D65Transmittance, D65 AOI Y L* a* b* AOI Y L* a* b* 0 0.7069 6.3854 −2.2225−1.0799 0 99.2661 99.7155 0.0176 0.246 1 0.7068 6.3845 −2.2203 −1.0789 199.2662 99.7156 0.0175 0.2459 2 0.7065 6.382 −2.2135 −1.0756 2 99.266499.7157 0.0172 0.2458 3 0.7061 6.3779 −2.2023 −1.0702 3 99.2669 99.71580.0167 0.2456 4 0.7055 6.3723 −2.1865 −1.0628 4 99.2675 99.7161 0.0160.2453 5 0.7047 6.3652 −2.1662 −1.0533 5 99.2683 99.7164 0.0151 0.245 60.7037 6.3569 −2.1415 −1.0419 6 99.2692 99.7167 0.014 0.2446 7 0.70276.3475 −2.1123 −1.0286 7 99.2702 99.7171 0.0127 0.2441 8 0.7016 6.3372−2.0788 −1.0136 8 99.2713 99.7176 0.0113 0.2436 9 0.7004 6.3264 −2.0408−0.9969 9 99.2725 99.718 0.0096 0.243 10 0.6991 6.3152 −1.9986 −0.978710 99.2737 99.7185 0.0077 0.2423 11 0.6979 6.3041 −1.9522 −0.9591 1199.2749 99.719 0.0057 0.2416 12 0.6967 6.2934 −1.9016 −0.9382 12 99.276199.7194 0.0034 0.2409 13 0.6956 6.2835 −1.8471 −0.9162 13 99.277299.7198 0.001 0.2401 14 0.6947 6.2749 −1.7887 −0.8932 14 99.2781 99.7202−0.0016 0.2393 15 0.6939 6.2681 −1.7267 −0.8694 15 99.2788 99.7205−0.0043 0.2385 16 0.6934 6.2636 −1.6611 −0.8449 16 99.2793 99.7207−0.0072 0.2377 17 0.6932 6.262 −1.5923 −0.8199 17 99.2794 99.7207−0.0103 0.2368 18 0.6935 6.2641 −1.5205 −0.7945 18 99.2792 99.7206−0.0135 0.236 19 0.6942 6.2705 −1.4458 −0.7688 19 99.2784 99.7203−0.0168 0.2351 20 0.6955 6.2819 −1.3687 −0.7431 20 99.2771 99.7198−0.0202 0.2343 21 0.6974 6.2993 −1.2894 −0.7174 21 99.2752 99.7191−0.0237 0.2335 22 0.7001 6.3236 −1.2084 −0.6919 22 99.2724 99.718−0.0273 0.2326 23 0.7036 6.3557 −1.1258 −0.6665 23 99.2688 99.7166−0.031 0.2319 24 0.7082 6.3967 −1.0423 −0.6414 24 99.2643 99.7148−0.0347 0.2311 25 0.7138 6.4477 −0.9582 −0.6164 25 99.2586 99.7126−0.0385 0.2303 26 0.7207 6.5102 −0.8741 −0.5915 26 99.2516 99.7099−0.0422 0.2296 27 0.729 6.5854 −0.7904 −0.5664 27 99.2432 99.7066−0.0459 0.2289 28 0.739 6.675 −0.7077 −0.5409 28 99.2333 99.7028 −0.04960.2281 29 0.7506 6.7805 −0.6266 −0.5147 29 99.2215 99.6982 −0.05330.2274 30 0.7643 6.9039 −0.5476 −0.4874 30 99.2078 99.6929 −0.05680.2266 31 0.7802 7.0472 −0.4712 −0.4586 31 99.1919 99.6867 −0.06020.2257 32 0.7985 7.2125 −0.398 −0.4279 32 99.1736 99.6796 −0.0635 0.224833 0.8195 7.4024 −0.3283 −0.395 33 99.1525 99.6714 −0.0667 0.2238 340.8435 7.6196 −0.2625 −0.3596 34 99.1284 99.662 −0.0697 0.2227 35 0.87097.8669 −0.2007 −0.3214 35 99.101 99.6513 −0.0725 0.2214 36 0.902 8.1468−0.1414 −0.2752 36 99.0698 99.6392 −0.0752 0.2201 37 0.9372 8.4567−0.0861 −0.2264 37 99.0346 99.6255 −0.0776 0.2186 38 0.9769 8.7973−0.0372 −0.1764 38 98.9948 99.61 −0.0799 0.217 39 1.0216 9.1699 0.0056−0.1256 39 98.9501 99.5926 −0.0821 0.2153 40 1.0718 9.5758 0.0426−0.0743 40 98.8998 99.573 −0.0841 0.2134 41 1.1281 10.0162 0.0743−0.0225 41 98.8434 99.5511 −0.0859 0.2113 42 1.1912 10.4922 0.101 0.029442 98.7803 99.5265 −0.0876 0.2091 43 1.2617 11.0049 0.1232 0.0814 4398.7098 99.4989 −0.0892 0.2066 44 1.3404 11.5553 0.1413 0.1336 44 98.63199.4682 −0.0907 0.2039 45 1.4283 12.1444 0.1557 0.1858 45 98.543199.4339 −0.0921 0.2009 46 1.5261 12.7732 0.1668 0.2381 46 98.445299.3957 −0.0934 0.1976 47 1.6351 13.4424 0.1751 0.2904 47 98.3362 99.353−0.0946 0.194 48 1.7564 14.1531 0.1811 0.3424 48 98.2148 99.3056 −0.09570.1899 49 1.8913 14.9062 0.1854 0.3938 49 98.0799 99.2528 −0.0968 0.185550 2.0413 15.7024 0.1885 0.4444 50 97.9299 99.194 −0.0979 0.1806 512.2079 16.5427 0.1911 0.4936 51 97.7632 99.1286 −0.0991 0.1753 52 2.393117.428 0.1938 0.5409 52 97.5781 99.0559 −0.1003 0.1695 53 2.5987 18.35920.197 0.5859 53 97.3724 98.975 −0.1017 0.1633 54 2.827 19.3372 0.20120.6283 54 97.1441 98.8851 −0.1033 0.1566 55 3.0804 20.363 0.2067 0.667655 96.8908 98.7851 −0.1051 0.1495 56 3.3616 21.4375 0.2139 0.7037 5696.6095 98.6739 −0.1073 0.1419 57 3.6737 22.5619 0.2227 0.7365 5796.2975 98.5503 −0.1098 0.1338 58 4.0199 23.7372 0.2332 0.7658 5895.9513 98.4129 −0.1128 0.1252 59 4.404 24.9646 0.2453 0.7917 59 95.567298.26 −0.1163 0.1162 60 4.8302 26.2453 0.2587 0.8141 60 95.1411 98.09−0.1203 0.1066 Reflectance color shift range between normal incidence(AOI = 0°) to AOI = 32° Low: 0.0024 High: 1.9375 Reflectance color shiftrange between normal incidence (AOI = 0°) and AOI = 33-60° Low: 2.0142High: 3.1215 Transmittance color shift range from normal incidence (AOI= 0°) to AOI = 60° Low: 0.0001 High: 0.1961

TABLE 11B One surface reflectance and transmitted color coordinates (Y,L*, a* and b*) using illuminant F2 for Example 5. Reflectance, F2Transmittance, F2 AOI Y L* a* b* AOI Y L* a* b* 0 0.6618 5.9781 −0.7261−2.007 0 99.3206 99.7367 −0.0204 0.3099 1 0.6618 5.9776 −0.7239 −2.006 199.3207 99.7367 −0.0205 0.3099 2 0.6616 5.9764 −0.7173 −2.0029 2 99.320899.7368 −0.0208 0.3098 3 0.6614 5.9743 −0.7063 −1.9975 3 99.321 99.7369−0.0213 0.3096 4 0.6611 5.9715 −0.6912 −1.9895 4 99.3213 99.737 −0.0220.3093 5 0.6607 5.9682 −0.6721 −1.9786 5 99.3217 99.7371 −0.0228 0.30896 0.6603 5.9644 −0.6492 −1.9641 6 99.3221 99.7373 −0.0238 0.3084 70.6599 5.9604 −0.623 −1.9452 7 99.3225 99.7375 −0.025 0.3077 8 0.65945.9564 −0.5939 −1.921 8 99.323 99.7376 −0.0262 0.3067 9 0.659 5.9526−0.5624 −1.8903 9 99.3234 99.7378 −0.0276 0.3056 10 0.6586 5.9495−0.5291 −1.8518 10 99.3237 99.7379 −0.0291 0.304 11 0.6584 5.9473−0.4947 −1.804 11 99.3239 99.738 −0.0306 0.3022 12 0.6583 5.9464 −0.4602−1.7451 12 99.324 99.738 −0.0321 0.2998 13 0.6584 5.9474 −0.4263 −1.673613 99.3239 99.738 −0.0336 0.2969 14 0.6588 5.9507 −0.3939 −1.588 1499.3235 99.7378 −0.0351 0.2935 15 0.6595 5.9569 −0.3639 −1.4872 1599.3228 99.7376 −0.0364 0.2893 16 0.6605 5.9667 −0.337 −1.3704 1699.3217 99.7371 −0.0376 0.2846 17 0.6621 5.9805 −0.3138 −1.2379 1799.3201 99.7365 −0.0387 0.2791 18 0.6642 5.9993 −0.2945 −1.0907 1899.3181 99.7357 −0.0396 0.2731 19 0.6669 6.0237 −0.2791 −0.9313 1999.3153 99.7347 −0.0403 0.2665 20 0.6703 6.0545 −0.2671 −0.7634 2099.3119 99.7333 −0.0409 0.2596 21 0.6745 6.0925 −0.2576 −0.5919 2199.3077 99.7317 −0.0414 0.2525 22 0.6796 6.1387 −0.2494 −0.423 2299.3025 99.7297 −0.0419 0.2456 23 0.6857 6.1939 −0.2409 −0.2638 2399.2964 99.7273 −0.0423 0.2391 24 0.6929 6.259 −0.2301 −0.1213 2499.2891 99.7245 −0.0429 0.2334 25 0.7013 6.3349 −0.2156 −0.0024 2599.2807 99.7212 −0.0436 0.2286 26 0.711 6.4227 −0.1957 0.0877 26 99.27199.7174 −0.0445 0.2251 27 0.7222 6.5235 −0.1697 0.1461 27 99.259899.7131 −0.0457 0.223 28 0.7349 6.6383 −0.1376 0.1729 28 99.247 99.7081−0.0472 0.2222 29 0.7493 6.7685 −0.1003 0.1718 29 99.2326 99.7025−0.0489 0.2227 30 0.7656 6.9156 −0.0602 0.1502 30 99.2163 99.6962−0.0507 0.224 31 0.7839 7.0812 −0.0203 0.1188 31 99.1979 99.689 −0.05250.2258 32 0.8046 7.2676 0.0152 0.0906 32 99.1772 99.681 −0.0541 0.227433 0.8277 7.4769 0.042 0.0793 33 99.154 99.672 −0.0554 0.2283 34 0.85387.712 0.0557 0.0975 34 99.128 99.6618 −0.0561 0.228 35 0.883 7.97610.0528 0.1547 35 99.0987 99.6504 −0.0561 0.226 36 0.9158 8.2697 0.03020.2513 36 99.0658 99.6377 −0.0552 0.2221 37 0.9527 8.5911 −0.0099 0.383137 99.0289 99.6233 −0.0536 0.2164 38 0.9941 8.9422 −0.0645 0.5402 3898.9875 99.6072 −0.0511 0.2093 39 1.0405 9.3246 −0.129 0.7072 39 98.94199.5891 −0.0481 0.2012 40 1.0925 9.7396 −0.1976 0.8659 40 98.889 99.5688−0.0446 0.193 41 1.1507 10.1883 −0.2644 0.9983 41 98.8308 99.5461−0.0409 0.1855 42 1.2155 10.6716 −0.3237 1.0895 42 98.7659 99.5208−0.0374 0.1794 43 1.2878 11.1899 −0.3713 1.1306 43 98.6936 99.4927−0.0342 0.1755 44 1.3681 11.7436 −0.4048 1.1201 44 98.6133 99.4613−0.0315 0.1739 45 1.4572 12.3332 −0.4237 1.0639 45 98.5242 99.4265−0.0295 0.1749 46 1.5559 12.9589 −0.4293 0.9737 46 98.4255 99.388−0.0281 0.1779 47 1.6651 13.6215 −0.4245 0.8651 47 98.3162 99.3452−0.0272 0.1824 48 1.786 14.3216 −0.4128 0.7541 48 98.1953 99.2979−0.0268 0.1876 49 1.9198 15.0605 −0.3977 0.6554 49 98.0615 99.2455−0.0265 0.1924 50 2.0679 15.8396 −0.3825 0.5796 50 97.9134 99.1875−0.0263 0.196 51 2.232 16.6606 −0.3695 0.5329 51 97.7492 99.1231 −0.02590.1978 52 2.414 17.5253 −0.3598 0.5165 52 97.5672 99.0516 −0.0251 0.197253 2.6161 18.4358 −0.3537 0.5274 53 97.3651 98.9721 −0.024 0.1942 542.8406 19.3939 −0.3505 0.5593 54 97.1406 98.8837 −0.0226 0.1888 553.0901 20.4013 −0.3488 0.6041 55 96.8911 98.7852 −0.0209 0.1816 563.3676 21.4598 −0.347 0.6535 56 96.6136 98.6755 −0.019 0.1731 57 3.676222.5706 −0.3435 0.6999 57 96.3051 98.5533 −0.0172 0.164 58 4.0192 23.735−0.3371 0.7375 58 95.962 98.4171 −0.0155 0.1548 59 4.4006 24.9539−0.3267 0.7627 59 95.5807 98.2654 −0.0143 0.1461 60 4.8243 26.2282−0.3118 0.7741 60 95.157 98.0963 −0.0136 0.1383 Reflectance color shiftrange between normal incidence (AOI = 0°) to AOI = 24° Low: 0.0024 High:1.9498 Reflectance color shift range between normal incidence (AOI = 0°)and AOI = 25-60° Low: 2.0685 High: 3.1576 Transmittance color shiftrange from normal incidence (AOI = 0°) to AOI = 60° Low: 0.0001 High:0.1717

TABLE 11C Two surface reflectance and transmitted color coordinates (Y,L*, a* and b*) using illuminant D65 for Example 5. Reflectance, D65Transmittance, D65 AOI Y L* a* b* AOI Y L* a* b* 0 4.7958 26.145 −0.7591−0.6773 0 95.1759 98.1039 0.0189 0.3086 1 4.7958 26.1448 −0.7584 −0.6771 95.176 98.1039 0.0188 0.3085 2 4.7955 26.144 −0.7564 −0.6761 2 95.176398.104 0.0185 0.3084 3 4.7951 26.1428 −0.7531 −0.6745 3 95.1767 98.10420.018 0.3082 4 4.7945 26.1412 −0.7484 −0.6724 4 95.1772 98.1044 0.01740.308 5 4.7939 26.1392 −0.7424 −0.6696 5 95.1779 98.1046 0.0165 0.3077 64.7931 26.137 −0.7351 −0.6663 6 95.1786 98.1049 0.0155 0.3073 7 4.792326.1347 −0.7264 −0.6625 7 95.1794 98.1053 0.0143 0.3068 8 4.7915 26.1323−0.7164 −0.6581 8 95.1802 98.1056 0.0128 0.3063 9 4.7907 26.1301 −0.705−0.6532 9 95.1809 98.1059 0.0113 0.3058 10 4.7901 26.1282 −0.6924−0.6479 10 95.1816 98.1061 0.0095 0.3052 11 4.7896 26.1268 −0.6785−0.6421 11 95.182 98.1063 0.0075 0.3045 12 4.7894 26.1261 −0.6633−0.6359 12 95.1822 98.1064 0.0054 0.3038 13 4.7895 26.1265 −0.6468−0.6294 13 95.1821 98.1063 0.0031 0.3031 14 4.7901 26.1281 −0.6292−0.6225 14 95.1815 98.1061 0.0006 0.3024 15 4.7912 26.1314 −0.6103−0.6153 15 95.1803 98.1056 −0.002 0.3016 16 4.7929 26.1365 −0.5904−0.6079 16 95.1785 98.1049 −0.0048 0.3009 17 4.7955 26.144 −0.5694−0.6003 17 95.176 98.1039 −0.0077 0.3001 18 4.799 26.1542 −0.5475−0.5924 18 95.1724 98.1025 −0.0107 0.2993 19 4.8035 26.1675 −0.5246−0.5844 19 95.1679 98.1006 −0.0139 0.2986 20 4.8093 26.1845 −0.501−0.5763 20 95.162 98.0983 −0.0172 0.2978 21 4.8166 26.2057 −0.4766−0.568 21 95.1547 98.0954 −0.0206 0.2971 22 4.8255 26.2316 −0.4516−0.5597 22 95.1458 98.0918 −0.024 0.2964 23 4.8362 26.2628 −0.4262−0.5513 23 95.1351 98.0875 −0.0275 0.2957 24 4.849 26.3 −0.4004 −0.542824 95.1222 98.0824 −0.0311 0.295 25 4.8641 26.344 −0.3745 −0.5342 2595.107 98.0763 −0.0347 0.2943 26 4.8819 26.3955 −0.3485 −0.5254 2695.0892 98.0692 −0.0383 0.2937 27 4.9025 26.4553 −0.3226 −0.5163 2795.0685 98.0609 −0.0419 0.2931 28 4.9265 26.5243 −0.2971 −0.5069 2895.0445 98.0513 −0.0454 0.2924 29 4.9541 26.6035 −0.2721 −0.497 2995.0168 98.0403 −0.0489 0.2918 30 4.9857 26.6939 −0.2478 −0.4866 3094.9852 98.0276 −0.0523 0.2911 31 5.0217 26.7965 −0.2244 −0.4755 3194.9491 98.0131 −0.0557 0.2903 32 5.0627 26.9127 −0.202 −0.4635 3294.908 97.9967 −0.0589 0.2895 33 5.1092 27.0435 −0.1807 −0.4506 3394.8615 97.9781 −0.0619 0.2887 34 5.1616 27.1904 −0.1607 −0.4368 3494.8089 97.957 −0.0648 0.2877 35 5.2208 27.3547 −0.142 −0.4219 3594.7497 97.9333 −0.0676 0.2866 36 5.2872 27.5379 −0.1245 −0.4059 3694.6832 97.9066 −0.0702 0.2854 37 5.3617 27.7415 −0.1084 −0.3889 3794.6086 97.8767 −0.0726 0.2841 38 5.4451 27.967 −0.0935 −0.3707 3894.5252 97.8432 −0.0749 0.2826 39 5.5382 28.2162 −0.0797 −0.3515 3994.432 97.8058 −0.0771 0.2811 40 5.6421 28.4909 −0.067 −0.3313 4094.3281 97.764 −0.0792 0.2794 41 5.7577 28.7927 −0.0553 −0.3099 4194.2124 97.7175 −0.0811 0.2775 42 5.8862 29.1234 −0.0445 −0.2874 4294.0838 97.6658 −0.083 0.2755 43 6.0288 29.4851 −0.0344 −0.2638 4393.9411 97.6082 −0.0848 0.2733 44 6.1871 29.8796 −0.025 −0.2391 4493.7828 97.5444 −0.0866 0.2708 45 6.3624 30.3088 −0.0162 −0.2132 4593.6074 97.4736 −0.0883 0.2682 46 6.5564 30.7748 −0.0079 −0.1862 4693.4133 97.3951 −0.09 0.2652 47 6.7709 31.2795 0.0001 −0.1581 47 93.198797.3082 −0.0918 0.262 48 7.0079 31.825 0.008 −0.129 48 92.9616 97.212−0.0936 0.2586 49 7.2697 32.4131 0.0158 −0.0992 49 92.6997 97.1056−0.0955 0.2548 50 7.5585 33.0459 0.0237 −0.0687 50 92.4109 96.988−0.0975 0.2507 51 7.8769 33.7253 0.032 −0.038 51 92.0923 96.858 −0.09970.2463 52 8.2279 34.4531 0.0408 −0.0072 52 91.7413 96.7144 −0.10220.2416 53 8.6144 35.2311 0.0502 0.0233 53 91.3546 96.5559 −0.1049 0.236754 9.0399 36.0611 0.0603 0.0532 54 90.929 96.3808 −0.108 0.2315 559.5081 36.9447 0.0713 0.0822 55 90.4608 96.1876 −0.1116 0.2262 5610.0229 37.8834 0.083 0.1101 56 89.946 95.9743 −0.1155 0.2206 57 10.588638.8787 0.0955 0.1366 57 89.3801 95.7391 −0.12 0.2149 58 11.21 39.93190.1086 0.1615 58 88.7586 95.4795 −0.1251 0.209 59 11.8922 41.0443 0.12210.1847 59 88.0763 95.1931 −0.1306 0.2031 60 12.6407 42.2168 0.1358 0.20660 87.3278 94.8772 −0.1368 0.1971 Reflectance color shift range betweennormal incidence (AOI = 0 degrees) to AOI = 60 degrees Low: 0.0007 High:1.2574 Transmittance color shift range from normal incidence (AOI = 0)to AOI = 60 Low: 0.0001 High: 0.1915

TABLE 11D Two surface reflectance and transmitted color coordinates (Y,L*, a* and b*) using illuminant F2 for Example 5. Reflectance, DF2Transmittance, DF2 AOI Y L* a* b* AOI Y L* a* b* 0 4.7462 25.999 −0.2777−1.0087 0 95.2355 98.1277 −0.0182 0.3798 1 4.7461 25.9989 −0.277 −1.00841 95.2355 98.1277 −0.0183 0.3797 2 4.746 25.9985 −0.275 −1.0075 295.2356 98.1277 −0.0186 0.3796 3 4.7458 25.9979 −0.2717 −1.0059 395.2358 98.1278 −0.019 0.3794 4 4.7455 25.9971 −0.2672 −1.0036 4 95.236198.1279 −0.0197 0.3792 5 4.7452 25.9963 −0.2615 −1.0004 5 95.2364 98.128−0.0205 0.3788 6 4.7449 25.9954 −0.2546 −0.9961 6 95.2367 98.1281−0.0214 0.3783 7 4.7447 25.9947 −0.2467 −0.9906 7 95.2369 98.1282−0.0225 0.3776 8 4.7445 25.9942 −0.238 −0.9835 8 95.2371 98.1283 −0.02370.3768 9 4.7445 25.9941 −0.2285 −0.9745 9 95.2371 98.1283 −0.025 0.375610 4.7447 25.9945 −0.2184 −0.9631 10 95.2369 98.1282 −0.0264 0.3742 114.7451 25.9958 −0.2081 −0.949 11 95.2365 98.1281 −0.0279 0.3725 124.7459 25.9982 −0.1977 −0.9315 12 95.2357 98.1277 −0.0293 0.3702 134.7471 26.0018 −0.1875 −0.9104 13 95.2344 98.1272 −0.0307 0.3675 144.7489 26.0071 −0.1777 −0.885 14 95.2326 98.1265 −0.0321 0.3643 154.7513 26.0142 −0.1686 −0.8551 15 95.2301 98.1255 −0.0334 0.3604 164.7545 26.0237 −0.1604 −0.8204 16 95.2269 98.1242 −0.0346 0.3559 174.7587 26.0359 −0.1533 −0.781 17 95.2228 98.1226 −0.0356 0.3508 184.7639 26.0511 −0.1474 −0.7373 18 95.2176 98.1205 −0.0364 0.3452 194.7703 26.0699 −0.1426 −0.6899 19 95.2111 98.1179 −0.0371 0.339 20 4.77826.0928 −0.1389 −0.6399 20 95.2033 98.1148 −0.0377 0.3325 21 4.787426.1202 −0.1358 −0.5888 21 95.1939 98.1111 −0.0382 0.326 22 4.798526.1528 −0.1331 −0.5384 22 95.1828 98.1066 −0.0386 0.3195 23 4.811626.191 −0.1303 −0.4909 23 95.1697 98.1014 −0.0391 0.3135 24 4.826826.2356 −0.1268 −0.4483 24 95.1544 98.0953 −0.0396 0.3081 25 4.844526.287 −0.1221 −0.4126 25 95.1367 98.0882 −0.0403 0.3038 26 4.864826.3461 −0.1159 −0.3852 26 95.1164 98.0801 −0.0412 0.3006 27 4.888126.4135 −0.1079 −0.3671 27 95.0931 98.0707 −0.0424 0.2987 28 4.914626.49 −0.0982 −0.3579 28 95.0665 98.0601 −0.0438 0.2981 29 4.944626.5764 −0.087 −0.3566 29 95.0364 98.0481 −0.0454 0.2986 30 4.978626.6737 −0.0751 −0.3608 30 95.0024 98.0345 −0.0472 0.3 31 5.0169 26.7828−0.0634 −0.3673 31 94.9641 98.0192 −0.0489 0.3018 32 5.0599 26.9049−0.0531 −0.3726 32 94.921 98.0019 −0.0504 0.3034 33 5.1083 27.0411−0.0453 −0.3727 33 94.8726 97.9825 −0.0516 0.3044 34 5.1625 27.1929−0.0413 −0.3643 34 94.8183 97.9608 −0.0523 0.3042 35 5.2233 27.3616−0.0417 −0.3452 35 94.7576 97.9364 −0.0523 0.3025 36 5.2912 27.5488−0.0472 −0.3145 36 94.6896 97.9092 −0.0516 0.2991 37 5.3672 27.7562−0.0576 −0.2729 37 94.6136 97.8787 −0.0502 0.2941 38 5.4519 27.9854−0.0722 −0.2232 38 94.5287 97.8446 −0.0481 0.2878 39 5.5465 28.2381−0.0899 −0.1692 39 94.4342 97.8067 −0.0455 0.2808 40 5.6517 28.5162−0.1092 −0.1157 40 94.3289 97.7643 −0.0425 0.2737 41 5.7687 28.8214−0.1283 −0.0678 41 94.2118 97.7173 −0.0395 0.2674 42 5.8986 29.1553−0.1456 −0.0298 42 94.0818 97.665 −0.0367 0.2625 43 6.0426 29.5197−0.1596 −0.0044 43 93.9378 97.6069 −0.0343 0.2594 44 6.2019 29.9162−0.1696 0.0071 44 93.7785 97.5427 −0.0324 0.2585 45 6.378 30.3467 −0.1750.0059 45 93.6024 97.4715 −0.0311 0.2596 46 6.5723 30.8128 −0.1762−0.0052 46 93.408 97.3929 −0.0306 0.2625 47 6.7867 31.3163 −0.1736−0.0222 47 93.1935 97.3061 −0.0305 0.2666 48 7.023 31.8593 −0.1682−0.0404 48 92.9571 97.2102 −0.031 0.2711 49 7.2835 32.4437 −0.1612−0.0552 49 92.6967 97.1044 −0.0318 0.2752 50 7.5704 33.0717 −0.1534−0.0632 50 92.4097 96.9875 −0.0327 0.2782 51 7.8865 33.7454 −0.1456−0.0622 51 92.0935 96.8585 −0.0336 0.2797 52 8.2348 34.4671 −0.1382−0.0514 52 91.7452 96.7161 −0.0345 0.2793 53 8.6184 35.2389 −0.1315−0.0316 53 91.3615 96.5587 −0.0353 0.277 54 9.0409 36.063 −0.1251−0.0045 54 90.9389 96.3849 −0.0361 0.2731 55 9.5062 36.9412 −0.11890.0272 55 90.4736 96.1929 −0.0369 0.2678 56 10.0184 37.8753 −0.11230.0609 56 89.9614 95.9807 −0.0378 0.2616 57 10.5818 38.867 −0.105 0.09457 89.3978 95.7464 −0.0389 0.255 58 11.2014 39.9175 −0.0964 0.1247 5888.7782 95.4877 −0.0405 0.2484 59 11.8821 41.028 −0.0864 0.1514 5988.0975 95.202 −0.0425 0.2422 60 12.6294 42.1994 −0.0747 0.1734 6087.3501 94.8866 −0.0452 0.2367 Reflectance color shift range betweennormal incidence (AOI = 0 degrees) to AOI = 60 degrees Low: 0.0007 High:1.1994 Transmittance color shift range from normal incidence (AOI = 0)to AOI = 60 Low: 0.0001 High: 0.1456

Example 6

Example 6 included the same strengthened aluminosilicate glass substrateas Example 5 and a coating a 12-layer optical coating including a 2micrometer scratch resistant layer, as show in Table 12.

TABLE 12 Structure of Example 6. Refractive Physical Coating/ Periods,if Index (at Thickness Layer applicable Material 550 nm) (nm) Ambient —Air medium SiO₂ 1.46929 91.46 Optical 1 AlO_(x)N_(y) 1.97879 154.26coating SiO₂ 1.46929 21.74 2 AlO_(x)N_(y) 1.97879 51.85 SiO₂ 1.4692914.03 Scratch- AlO_(x)N_(y) 1.97879 2000 Resistant Layer 1 SiO₂ 1.469298.51 AlO_(x)N_(y) 1.97879 43.16 2 SiO₂ 1.46929 28.82 AlO_(x)N_(y)1.97879 25.49 3 SiO₂ 1.46929 49.24 AlO_(x)N_(y) 1.97879 8.49 — — ASGlass 1.50542 Total coating thickness 2497.06

Example 6 exhibited a single side photopic average reflectance (i.e.,measured from the anti-reflective surface 122) over the opticalwavelength regime under D65 illumination at incident illumination anglesof 0 °, 30°, 45° and 60°, of 0.73%, 0.80%, 1.47%, and 4.85%,respectively. Example 6 exhibited a single side photopic averagetransmittance (i.e., measured through the anti-reflective surface 122)over the optical wavelength regime under D65 illumination at incidentillumination angles of 0 °, 30 °, 45° and 60°, of 99.26%, 99.18%,98.52%, and 95.13%, respectively.

Example 6 exhibited a total photopic average reflectance (i.e., measuredfrom the anti-reflective surface 122 and the opposite major surface 114)over the optical wavelength regime under D65 illumination at incidentillumination angles of 0 °, 30°, 45° and 60°, of 4.74%, 4.94%, 6.32%,and 12.56%, respectively. Example 6 exhibited a total photopic averagetransmittance (i.e., measured through the anti-reflective surface 122and the opposite major surface 114) over the optical wavelength regimeat incident illumination angles of 0 °, 30 °, 45° and 60°, of 95.24%,95.04%, 93.67%, and 87.42%, respectively.

The reflectance and transmitted color coordinates for a single surface(i.e., anti-reflective surface 122) and two surfaces (i.e.,anti-reflective surface 122 and major surface 114, of FIG. 1) of Example6, under incident illumination angles or AOI from 0 degrees to 60degrees and illuminants D65 and F2 are shown in Tables 13A-13D, in thesame manner as Example 5. The color shift is also calculated in the samemanner as Example 5.

TABLE 13A One surface reflectance and transmitted color coordinates (Y,L*, a* and b*) using illuminant D65 for Example 6. Reflectance, D65Transmittance, D65 AOI Y L* a* b* AOI Y L* a* b* 0 0.7252 6.5505 −1.1881−1.8063 0 99.2597 99.7131 −0.0079 0.2173 1 0.7251 6.5499 −1.1857 −1.8071 99.2598 99.7131 −0.008 0.2174 2 0.7249 6.5482 −1.1786 −1.8091 2 99.2699.7132 −0.0083 0.2175 3 0.7246 6.5454 −1.1667 −1.8126 3 99.2603 99.7133−0.0088 0.2177 4 0.7242 6.5415 −1.1503 −1.8175 4 99.2607 99.7134 −0.00950.2179 5 0.7237 6.5368 −1.1292 −1.8236 5 99.2612 99.7136 −0.0105 0.21826 0.7231 6.5313 −1.1038 −1.831 6 99.2618 99.7139 −0.0116 0.2186 7 0.72246.5252 −1.0741 −1.8393 7 99.2625 99.7141 −0.0129 0.219 8 0.7217 6.5187−1.0403 −1.8487 8 99.2632 99.7144 −0.0144 0.2195 9 0.7209 6.512 −1.0026−1.8588 9 99.2639 99.7147 −0.016 0.22 10 0.7202 6.5055 −0.9613 −1.869410 99.2647 99.715 −0.0179 0.2206 11 0.7195 6.4993 −0.9166 −1.8804 1199.2653 99.7152 −0.0198 0.2211 12 0.7189 6.494 −0.8689 −1.8915 1299.2659 99.7155 −0.0219 0.2217 13 0.7185 6.4898 −0.8186 −1.9023 1399.2664 99.7156 −0.0241 0.2223 14 0.7182 6.4872 −0.766 −1.9126 1499.2666 99.7157 −0.0264 0.2229 15 0.7181 6.4867 −0.7116 −1.922 1599.2667 99.7158 −0.0288 0.2234 16 0.7183 6.4887 −0.6558 −1.93 16 99.266499.7157 −0.0313 0.2239 17 0.7189 6.4939 −0.5991 −1.9363 17 99.265899.7154 −0.0338 0.2243 18 0.7199 6.5028 −0.542 −1.9404 18 99.2648 99.715−0.0363 0.2247 19 0.7214 6.5162 −0.4851 −1.9418 19 99.2633 99.7145−0.0389 0.2249 20 0.7234 6.5348 −0.429 −1.94 20 99.2613 99.7136 −0.04130.225 21 0.7262 6.5593 −0.3741 −1.9346 21 99.2585 99.7126 −0.0438 0.22522 0.7296 6.5907 −0.321 −1.9251 22 99.255 99.7112 −0.0462 0.2248 230.734 6.63 −0.2702 −1.9109 23 99.2506 99.7095 −0.0484 0.2244 24 0.73936.6782 −0.2223 −1.8917 24 99.2453 99.7074 −0.0506 0.2238 25 0.74586.7363 −0.1777 −1.8669 25 99.2388 99.7049 −0.0526 0.2229 26 0.75346.8058 −0.1368 −1.8362 26 99.2311 99.7019 −0.0544 0.2218 27 0.76256.8879 −0.1001 −1.7991 27 99.222 99.6984 −0.0561 0.2205 28 0.7732 6.9842−0.0679 −1.7553 28 99.2113 99.6942 −0.0576 0.2188 29 0.7856 7.0962−0.0403 −1.7038 29 99.1989 99.6894 −0.0589 0.2169 30 0.7999 7.2258−0.0178 −1.6435 30 99.1845 99.6838 −0.06 0.2146 31 0.8164 7.3749 −0.0005−1.5735 31 99.168 99.6774 −0.0608 0.212 32 0.8354 7.5457 0.0115 −1.492632 99.149 99.67 −0.0614 0.2091 33 0.8569 7.7406 0.018 −1.3996 33 99.127499.6616 −0.0618 0.2058 34 0.8815 7.9621 0.0189 −1.2929 34 99.102999.6521 −0.062 0.2021 35 0.9093 8.2114 0.014 −1.1738 35 99.075 99.6412−0.0619 0.198 36 0.9407 8.4872 0.0038 −1.0477 36 99.0436 99.629 −0.06160.1936 37 0.9761 8.791 −0.0111 −0.9156 37 99.0081 99.6152 −0.061 0.188738 1.016 9.1241 −0.0303 −0.7785 38 98.9682 99.5997 −0.0602 0.1834 391.0608 9.4881 −0.0532 −0.6376 39 98.9234 99.5822 −0.0592 0.1777 401.1111 9.8844 −0.079 −0.4943 40 98.8731 99.5626 −0.0579 0.1717 41 1.167310.3142 −0.107 −0.3501 41 98.8168 99.5407 −0.0565 0.1652 42 1.230310.7788 −0.1365 −0.2065 42 98.7538 99.5161 −0.0548 0.1583 43 1.300611.2795 −0.1664 −0.065 43 98.6835 99.4887 −0.053 0.1511 44 1.379 11.8175−0.1961 0.0727 44 98.605 99.4581 −0.0511 0.1436 45 1.4665 12.3937−0.2245 0.2053 45 98.5175 99.4239 −0.049 0.1357 46 1.564 13.0093 −0.2510.3316 46 98.42 99.3858 −0.0468 0.1276 47 1.6725 13.6652 −0.2748 0.450547 98.3114 99.3434 −0.0447 0.1192 48 1.7932 14.3625 −0.2952 0.5612 4898.1907 99.2961 −0.0425 0.1105 49 1.9275 15.1021 −0.3117 0.663 4998.0564 99.2436 −0.0404 0.1016 50 2.0767 15.8849 −0.324 0.7555 5097.9072 99.1851 −0.0384 0.0925 51 2.2425 16.7118 −0.3317 0.8384 5197.7414 99.12 −0.0366 0.0832 52 2.4267 17.5838 −0.3348 0.9118 52 97.557299.0476 −0.035 0.0737 53 2.6312 18.5019 −0.3334 0.9756 53 97.352798.9672 −0.0336 0.064 54 2.8583 19.4671 −0.3276 1.0302 54 97.125698.8777 −0.0325 0.0541 55 3.1103 20.4803 −0.3178 1.0758 55 96.873698.7783 −0.0317 0.0441 56 3.39 21.5427 −0.3043 1.1128 56 96.5939 98.6677−0.0313 0.0339 57 3.7004 22.6553 −0.2875 1.1416 57 96.2835 98.5448−0.0313 0.0235 58 4.0449 23.8193 −0.268 1.1627 58 95.939 98.408 −0.03160.0131 59 4.4271 25.0359 −0.2462 1.1766 59 95.5569 98.2559 −0.03240.0024 60 4.8511 26.3063 −0.2227 1.1837 60 95.1328 98.0866 −0.03360.0083 Reflectance color shift range between normal incidence (AOI = 0degrees) to AOI = 42 degrees Low: 0.0007 High: 1.1994 Reflectance colorshift range between normal incidence (AOI = 0 degrees) and AOI = 43-60degrees Low: 2.0189 High: 3.1420 Transmittance color shift range fromnormal incidence (AOI = 0) to AOI = 60 Low: 0.0001 High: 0.2271

TABLE 13B One surface reflectance and transmitted color coordinates (Y,L*, a* and b*) using illuminant F2 for Example 6. Reflectance, F2Transmittance, F2 AOI Y L* a* b* AOI Y L* a* b* 0 0.7101 6.4142 −0.7229−1.0759 0 99.2803 99.721 −0.0074 0.2018 1 0.7101 6.4142 −0.7216 −1.07761 99.2803 99.721 −0.0075 0.2019 2 0.7101 6.414 −0.7176 −1.0828 2 99.280399.721 −0.0077 0.2021 3 0.7101 6.4139 −0.7111 −1.0916 3 99.2803 99.721−0.008 0.2025 4 0.71 6.4137 −0.702 −1.1041 4 99.2803 99.7211 −0.00840.2031 5 0.71 6.4136 −0.6902 −1.1207 5 99.2803 99.7211 −0.0089 0.2039 60.71 6.4138 −0.6757 −1.1414 6 99.2803 99.721 −0.0095 0.2048 7 0.71016.4144 −0.6587 −1.1666 7 99.2802 99.721 −0.0103 0.206 8 0.7102 6.4154−0.6389 −1.1967 8 99.2801 99.721 −0.0111 0.2073 9 0.7104 6.4172 −0.6165−1.2317 9 99.2799 99.7209 −0.0121 0.2089 10 0.7107 6.4199 −0.5914 −1.27210 99.2796 99.7208 −0.0132 0.2108 11 0.7111 6.4236 −0.5637 −1.3176 1199.2792 99.7206 −0.0144 0.2128 12 0.7117 6.4287 −0.5335 −1.3683 1299.2786 99.7204 −0.0158 0.2152 13 0.7124 6.4354 −0.5008 −1.4239 1399.2779 99.7201 −0.0172 0.2177 14 0.7134 6.4438 −0.466 −1.4836 1499.2769 99.7197 −0.0187 0.2204 15 0.7145 6.4544 −0.4291 −1.5465 1599.2757 99.7193 −0.0204 0.2232 16 0.716 6.4673 −0.3908 −1.6112 1699.2743 99.7187 −0.0221 0.2262 17 0.7177 6.4829 −0.3513 −1.676 1799.2726 99.718 −0.0238 0.2292 18 0.7198 6.5016 −0.3112 −1.7386 1899.2705 99.7172 −0.0256 0.232 19 0.7222 6.5238 −0.2713 −1.7967 19 99.26899.7163 −0.0273 0.2347 20 0.7251 6.5501 −0.2323 −1.8477 20 99.265199.7151 −0.029 0.2371 21 0.7286 6.581 −0.1949 −1.889 21 99.2617 99.7138−0.0307 0.2391 22 0.7326 6.6174 −0.16 −1.918 22 99.2576 99.7122 −0.03230.2406 23 0.7373 6.6601 −0.1284 −1.9329 23 99.2529 99.7104 −0.03370.2414 24 0.7429 6.7103 −0.1008 −1.9321 24 99.2473 99.7082 −0.03490.2417 25 0.7494 6.7693 −0.0778 −1.9154 25 99.2408 99.7057 −0.036 0.241226 0.7571 6.8387 −0.0598 −1.883 26 99.2331 99.7027 −0.0368 0.2401 270.7661 6.9201 −0.047 −1.8367 27 99.224 99.6992 −0.0374 0.2383 28 0.77677.0156 −0.0397 −1.7786 28 99.2134 99.6951 −0.0378 0.2361 29 0.789 7.1274−0.0376 −1.7112 29 99.201 99.6902 −0.038 0.2335 30 0.8035 7.2578 −0.0409−1.6375 30 99.1866 99.6846 −0.0379 0.2307 31 0.8203 7.4094 −0.0493−1.5601 31 99.1698 99.6781 −0.0376 0.2279 32 0.8397 7.5847 −0.0628−1.4804 32 99.1504 99.6705 −0.0371 0.2251 33 0.862 7.7865 −0.0814−1.3984 33 99.128 99.6618 −0.0364 0.2223 34 0.8876 8.0175 −0.1055−1.3122 34 99.1024 99.6519 −0.0354 0.2197 35 0.9167 8.277 −0.132 −1.223835 99.0733 99.6406 −0.0342 0.2172 36 0.9496 8.564 −0.1627 −1.1341 3699.0404 99.6278 −0.0328 0.2145 37 0.9866 8.8793 −0.1972 −1.0402 3799.0033 99.6133 −0.0311 0.2116 38 1.0281 9.2231 −0.2346 −0.9392 3898.9619 99.5972 −0.0291 0.2083 39 1.0743 9.5959 −0.2741 −0.8287 3998.9156 99.5792 −0.0269 0.2043 40 1.1258 9.998 −0.3141 −0.7076 4098.8641 99.5591 −0.0246 0.1996 41 1.1828 10.4299 −0.3529 −0.5766 4198.8071 99.5369 −0.0221 0.1942 42 1.246 10.8925 −0.3887 −0.4377 4298.7438 99.5122 −0.0196 0.1879 43 1.316 11.3867 −0.4195 −0.2946 4398.6739 99.4849 −0.0172 0.181 44 1.3934 11.9138 −0.4437 −0.1519 4498.5964 99.4547 −0.0149 0.1735 45 1.4793 12.4757 −0.4603 −0.014 4598.5105 99.4212 −0.0129 0.1658 46 1.5745 13.0742 −0.469 0.1151 4698.4153 99.384 −0.0113 0.158 47 1.6803 13.7114 −0.47 0.2325 47 98.309499.3426 −0.01 0.1503 48 1.798 14.3895 −0.4646 0.3374 48 98.1917 99.2965−0.0089 0.1427 49 1.9291 15.1106 −0.4545 0.4304 49 98.0607 99.2452−0.0082 0.1352 50 2.0752 15.8768 −0.4419 0.5135 50 97.9146 99.188−0.0075 0.1277 51 2.238 16.6898 −0.4288 0.5895 51 97.7517 99.1241−0.0069 0.1199 52 2.4196 17.5511 −0.4171 0.6614 52 97.5701 99.0527−0.0061 0.1116 53 2.622 18.4618 −0.4078 0.7317 53 97.3677 98.9731 −0.0050.1026 54 2.8476 19.4228 −0.4015 0.8015 54 97.1421 98.8843 −0.00350.0926 55 3.0986 20.4347 −0.398 0.871 55 96.8911 98.7852 −0.0017 0.081656 3.3779 21.4979 −0.3962 0.9389 56 96.6118 98.6748 0.0005 0.0694 573.6883 22.613 −0.3949 1.0028 57 96.3014 98.5519 0.003 0.0564 58 4.03323.7801 −0.3923 1.06 58 95.9568 98.4151 0.0055 0.0427 59 4.4155 25−0.3869 1.1077 59 95.5743 98.2628 0.0078 0.0286 60 4.8397 26.2731−0.3773 1.1433 60 95.1501 98.0935 0.0098 0.0147 Reflectance color shiftrange between normal incidence (AOI = 0 degrees) to AOI = 55 degreesLow: 0.0021 High: 1.9738 Reflectance color shift range between normalincidence (AOI = 0 degrees) and AOI = 56-60 degrees Low: 2.0412 High:2.2459 Transmittance color shift range from normal incidence (AOI = 0)to AOI = 60 Low: 0.0001 High: 0.1879

TABLE 13C Two surface reflectance and transmitted color coordinates (Y,L*, a* and b*) using illuminant D65 for Example 6. Reflectance, D65Transmittance, D65 AOI Y L* a* b* AOI Y L* a* b* 0 4.7393 25.9789−0.4402 −0.9295 0 95.2449 98.1314 −0.0038 0.2771 1 4.7393 25.9787−0.4395 −0.9297 1 95.245 98.1315 −0.0039 0.2771 2 4.7391 25.9782 −0.4374−0.9303 2 95.2452 98.1315 −0.0042 0.2772 3 4.7388 25.9774 −0.4338−0.9314 3 95.2454 98.1316 −0.0047 0.2774 4 4.7385 25.9763 −0.4289−0.9328 4 95.2458 98.1318 −0.0054 0.2776 5 4.738 25.975 −0.4226 −0.93475 95.2462 98.132 −0.0062 0.2779 6 4.7376 25.9736 −0.4149 −0.9368 695.2467 98.1321 −0.0073 0.2783 7 4.7371 25.9722 −0.406 −0.9393 7 95.247298.1323 −0.0085 0.2787 8 4.7367 25.971 −0.3958 −0.942 8 95.2476 98.1325−0.0099 0.2791 9 4.7363 25.97 −0.3845 −0.945 9 95.2479 98.1326 −0.01150.2796 10 4.7361 25.9694 −0.372 −0.948 10 95.2481 98.1327 −0.0132 0.280111 4.7362 25.9695 −0.3585 −0.9512 11 95.248 98.1327 −0.0151 0.2807 124.7365 25.9704 −0.3441 −0.9543 12 95.2477 98.1325 −0.0171 0.2812 134.7372 25.9725 −0.3289 −0.9572 13 95.247 98.1323 −0.0192 0.2818 144.7383 25.9759 −0.313 −0.96 14 95.2458 98.1318 −0.0214 0.2823 15 4.740125.981 −0.2965 −0.9623 15 95.2441 98.1311 −0.0237 0.2829 16 4.742525.9881 −0.2795 −0.9641 16 95.2417 98.1301 −0.026 0.2833 17 4.745725.9975 −0.2623 −0.9653 17 95.2384 98.1288 −0.0284 0.2837 18 4.749826.0098 −0.245 −0.9657 18 95.2343 98.1272 −0.0308 0.2841 19 4.75526.0252 −0.2277 −0.9651 19 95.229 98.1251 −0.0332 0.2843 20 4.761526.0443 −0.2106 −0.9634 20 95.2225 98.1225 −0.0355 0.2844 21 4.769426.0675 −0.1939 −0.9604 21 95.2146 98.1193 −0.0379 0.2843 22 4.77926.0956 −0.1778 −0.9559 22 95.205 98.1155 −0.0401 0.2841 23 4.790326.1289 −0.1624 −0.9497 23 95.1936 98.1109 −0.0423 0.2837 24 4.803826.1683 −0.1478 −0.9418 24 95.1802 98.1056 −0.0443 0.2831 25 4.819526.2143 −0.1342 −0.9319 25 95.1644 98.0993 −0.0462 0.2823 26 4.837926.2679 −0.1218 −0.92 26 95.146 98.0919 −0.048 0.2812 27 4.8592 26.3297−0.1107 −0.9058 27 95.1247 98.0834 −0.0496 0.2799 28 4.8836 26.4006−0.1008 −0.8893 28 95.1002 98.0736 −0.051 0.2783 29 4.9117 26.4817−0.0924 −0.8703 29 95.0721 98.0624 −0.0523 0.2764 30 4.9437 26.5739−0.0855 −0.8489 30 95.04 98.0495 −0.0533 0.2742 31 4.9802 26.6782 −0.08−0.8248 31 95.0036 98.0349 −0.0542 0.2717 32 5.0215 26.7959 −0.0761−0.798 32 94.9622 98.0184 −0.0548 0.2689 33 5.0682 26.9282 −0.0736−0.7686 33 94.9155 97.9997 −0.0552 0.2657 34 5.1208 27.0763 −0.0726−0.7364 34 94.8628 97.9786 −0.0554 0.2622 35 5.18 27.2417 −0.0731−0.7015 35 94.8035 97.9549 −0.0555 0.2583 36 5.2465 27.4257 −0.0749−0.6641 36 94.7371 97.9282 −0.0553 0.2541 37 5.3208 27.6299 −0.0779−0.6241 37 94.6627 97.8984 −0.0549 0.2495 38 5.404 27.856 −0.082 −0.581738 94.5795 97.865 −0.0544 0.2446 39 5.4967 28.1055 −0.0872 −0.5372 3994.4867 97.8278 −0.0536 0.2393 40 5.6001 28.3803 −0.0931 −0.4909 4094.3833 97.7862 −0.0528 0.2338 41 5.7151 28.682 −0.0996 −0.443 4194.2682 97.74 −0.0518 0.2279 42 5.8429 29.0127 −0.1065 −0.394 42 94.140497.6885 −0.0507 0.2217 43 5.9848 29.3741 −0.1134 −0.3441 43 93.998497.6314 −0.0495 0.2153 44 6.1421 29.7683 −0.1202 −0.294 44 93.841197.5679 −0.0484 0.2087 45 6.3164 30.1971 −0.1264 −0.2439 45 93.666797.4975 −0.0472 0.2019 46 6.5093 30.6627 −0.1318 −0.1944 46 93.473897.4196 −0.0461 0.195 47 6.7226 31.1669 −0.1361 −0.1458 47 93.260597.3332 −0.0451 0.188 48 6.9583 31.7118 −0.139 −0.0987 48 93.024797.2376 −0.0443 0.181 49 7.2186 32.2994 −0.1403 −0.0532 49 92.764497.1319 −0.0438 0.1739 50 7.5058 32.9316 −0.1398 −0.0099 50 92.477297.015 −0.0435 0.1668 51 7.8225 33.6104 −0.1372 0.0311 51 92.160496.8858 −0.0435 0.1598 52 8.1715 34.3376 −0.1327 0.0694 52 91.811396.7431 −0.044 0.1529 53 8.556 35.115 −0.126 0.1049 53 91.4268 96.5855−0.0448 0.146 54 8.9793 35.9445 −0.1174 0.1374 54 91.0034 96.4114−0.0462 0.1393 55 9.4451 36.8276 −0.1069 0.1667 55 90.5376 96.2193−0.048 0.1328 56 9.9574 37.7659 −0.0948 0.1928 56 90.0252 96.0072−0.0503 0.1265 57 10.5205 38.7609 −0.0812 0.2157 57 89.4621 95.7732−0.0532 0.1204 58 11.1392 39.8139 −0.0664 0.2354 58 88.8433 95.5149−0.0566 0.1145 59 11.8185 40.9263 −0.0508 0.2518 59 88.1639 95.2299−0.0605 0.1089 60 12.5641 42.099 −0.0347 0.2652 60 87.4183 94.9155−0.0649 0.1037 Reflectance color shift range between normal incidence(AOI = 0 degrees) to AOI = 60 degrees Low: 0.0007 High: 1.2616Transmittance color shift range from normal incidence (AOI = 0) to AOI =60 Low: 0.0001 High: 0.1838

TABLE 13D Two surface reflectance and transmitted color coordinates (Y,L*, a* and b*) using illuminant F2 for Example 6. Reflectance, F2Transmittance, F2 AOI Y L* a* b* AOI Y L* a* b* 0 4.717 25.9128 −0.2697−0.7766 0 95.2729 98.1426 −0.005 0.2726 1 4.717 25.9128 −0.2693 −0.77711 95.273 98.1426 −0.005 0.2726 2 4.717 25.9128 −0.2682 −0.7786 2 95.27398.1426 −0.0052 0.2729 3 4.717 25.9128 −0.2662 −0.7812 3 95.273 98.1426−0.0055 0.2733 4 4.717 25.9128 −0.2634 −0.7849 4 95.273 98.1426 −0.00580.2738 5 4.717 25.9129 −0.2599 −0.7897 5 95.2729 98.1426 −0.0063 0.27456 4.7172 25.9132 −0.2555 −0.7958 6 95.2728 98.1426 −0.0069 0.2754 74.7174 25.9139 −0.2503 −0.8031 7 95.2726 98.1425 −0.0076 0.2765 8 4.717725.9149 −0.2444 −0.8119 8 95.2722 98.1423 −0.0085 0.2778 9 4.718225.9164 −0.2376 −0.8221 9 95.2717 98.1421 −0.0094 0.2793 10 4.71925.9186 −0.23 −0.8338 10 95.271 98.1418 −0.0104 0.2811 11 4.72 25.9217−0.2216 −0.847 11 95.2699 98.1414 −0.0116 0.283 12 4.7214 25.9258−0.2124 −0.8617 12 95.2685 98.1409 −0.0129 0.2852 13 4.7232 25.9311−0.2025 −0.8777 13 95.2667 98.1401 −0.0142 0.2876 14 4.7255 25.9379−0.192 −0.8948 14 95.2644 98.1392 −0.0157 0.2902 15 4.7283 25.9463−0.1808 −0.9127 15 95.2616 98.1381 −0.0172 0.2929 16 4.7318 25.9567−0.1691 −0.9311 16 95.258 98.1367 −0.0188 0.2957 17 4.7361 25.9693−0.1571 −0.9492 17 95.2538 98.135 −0.0204 0.2985 18 4.7412 25.9845−0.145 −0.9666 18 95.2486 98.1329 −0.0221 0.3012 19 4.7474 26.0025−0.1329 −0.9825 19 95.2425 98.1305 −0.0238 0.3037 20 4.7546 26.0239−0.1211 −0.996 20 95.2352 98.1275 −0.0254 0.306 21 4.7632 26.0491−0.1097 −1.0064 21 95.2266 98.1241 −0.027 0.3079 22 4.7732 26.0786−0.0992 −1.0129 22 95.2166 98.1201 −0.0285 0.3092 23 4.7849 26.113−0.0896 −1.015 23 95.2048 98.1154 −0.0298 0.31 24 4.7986 26.153 −0.0813−1.0123 24 95.1912 98.11 −0.031 0.3102 25 4.8144 26.1993 −0.0743 −1.004525 95.1753 98.1036 −0.032 0.3097 26 4.8327 26.2528 −0.0688 −0.9919 2695.157 98.0963 −0.0328 0.3086 27 4.8539 26.3144 −0.0649 −0.9749 2795.1358 98.0878 −0.0334 0.307 28 4.8783 26.3852 −0.0625 −0.9542 2895.1114 98.0781 −0.0338 0.3048 29 4.9063 26.4662 −0.0617 −0.9306 2995.0833 98.0669 −0.0339 0.3024 30 4.9384 26.5586 −0.0623 −0.9053 3095.0512 98.054 −0.0339 0.2997 31 4.9751 26.6637 −0.0644 −0.879 3195.0145 98.0393 −0.0337 0.297 32 5.0169 26.7827 −0.0678 −0.8525 3294.9727 98.0226 −0.0332 0.2943 33 5.0642 26.917 −0.0725 −0.8262 3394.9253 98.0036 −0.0326 0.2917 34 5.1178 27.0677 −0.0785 −0.8001 3494.8718 97.9822 −0.0318 0.2892 35 5.1781 27.2362 −0.0858 −0.7738 3594.8114 97.958 −0.0307 0.2867 36 5.2458 27.4238 −0.0943 −0.7466 3694.7437 97.9309 −0.0295 0.2842 37 5.3215 27.6318 −0.104 −0.7174 3794.668 97.9005 −0.0281 0.2814 38 5.406 27.8614 −0.1147 −0.6852 3894.5835 97.8666 −0.0264 0.2782 39 5.5 28.1141 −0.1262 −0.6492 39 94.489597.8289 −0.0246 0.2745 40 5.6043 28.3912 −0.1379 −0.609 40 94.385197.787 −0.0227 0.2701 41 5.7198 28.6943 −0.1494 −0.5645 41 94.269597.7405 −0.0208 0.265 42 5.8477 29.025 −0.1601 −0.5163 42 94.1416 97.689−0.0189 0.2593 43 5.9892 29.3852 −0.1692 −0.4654 43 94.0001 97.632−0.0172 0.2531 44 6.1455 29.7767 −0.1762 −0.4132 44 93.8438 97.569−0.0157 0.2466 45 6.3183 30.2017 −0.1807 −0.3611 45 93.671 97.4993−0.0146 0.2399 46 6.5092 30.6624 −0.1825 −0.3104 46 93.48 97.4221−0.0138 0.2333 47 6.7202 31.1612 −0.1815 −0.2619 47 93.269 97.3367−0.0135 0.2268 48 6.9533 31.7004 −0.1782 −0.2162 48 93.0359 97.2421−0.0135 0.2205 49 7.211 32.2825 −0.173 −0.1729 49 92.7781 97.1375−0.0138 0.2145 50 7.4957 32.9098 −0.1667 −0.1317 50 92.4934 97.0216−0.0143 0.2085 51 7.8103 33.5846 −0.1598 −0.0917 51 92.1788 96.8934−0.0149 0.2024 52 8.1575 34.3088 −0.153 −0.0522 52 91.8315 96.7514−0.0155 0.1961 53 8.5407 35.0845 −0.1466 −0.0127 53 91.4483 96.5943−0.0161 0.1894 54 8.9632 35.9134 −0.1408 0.0269 54 91.0258 96.4207−0.0165 0.1821 55 9.4287 36.7969 −0.1354 0.0662 55 90.5603 96.2287−0.0169 0.1744 56 9.941 37.7364 −0.1301 0.1044 56 90.0479 96.0166−0.0172 0.1663 57 10.5046 38.7332 −0.1243 0.1404 57 89.4843 95.7825−0.0177 0.1581 58 11.1238 39.7882 −0.1175 0.1729 58 88.865 95.524−0.0184 0.1499 59 11.8037 40.9025 −0.1092 0.2009 59 88.1851 95.2388−0.0197 0.1422 60 12.5498 42.0769 −0.099 0.2235 60 87.439 94.9242−0.0215 0.1353 Reflectance color shift range between normal incidence(AOI = 0 degrees) to AOI = 60 degrees Low: 0.0006 High: 1.0146Transmittance color shift range from normal incidence (AOI = 0) to AOI =60 Low: 0 High: 0.1383

Example 7

Example 7 included the same strengthened aluminosilicate glass substrateas Example 5 and a coating a 12-layer optical coating including a 2micrometer scratch resistant layer, as show in Table 14.

TABLE 14 Structure of Example 7. Refractive Physical Coating/ Periods,if Index (at Thickness Layer applicable Material 550 nm) (nm) Ambient —Air medium Optical 1 SiO₂ 1.48623 86.6 coating Si_(u)Al_(v)O_(x)N_(y)2.03056 145.8 2 SiO₂ 1.48623 19.2 Si_(u)Al_(v)O_(x)N_(y) 2.03056 48.0SiO₂ 1.48623 11.7 Scratch- Si_(u)Al_(v)O_(x)N_(y) 2.03056 2000.0Resistant Layer 1 SiO₂ 1.48623 10.2 Si_(u)Al_(v)O_(x)N_(y) 2.03056 42.02 SiO₂ 1.48623 32.7 Si_(u)Al_(v)O_(x)N_(y) 2.03056 23.6 3 SiO₂ 1.4862355.0 Si_(u)Al_(v)O_(x)N_(y) 2.03056 7.4 — — AS Glass 1.511 Total coatingthickness 2482.16

Modeled Examples 8-11

Modeled Examples 8-11 used modeling to demonstrate the reflectancespectra of articles that included embodiments of a durable andscratch-resistant optical coating, as described herein. In ModeledExamples 8-11 the optical coating included AlO_(x)N_(y) and SiO₂ layers,and a strengthened aluminosilicate glass substrate having a nominalcomposition of about 58 mol % SiO₂, 17 mol % Al₂O₃, 17 mol % Na₂O, 3 mol% MgO, 0.1 mol % SnO, and 6.5 mol % P₂O₅, as shown in Tables 15-19.Refractive index dispersion curves for coating materials and substrateused for Modeled Examples 8-11 were obtained in a similar manner asModeled Examples 2-5.

TABLE 15 Structure of Modeled Example 8. Refractive Physical Coating/Periods, if Index (at Thickness Layer applicable Material 550 nm) (nm)Ambient — Air 1 medium Optical 1 AlO_(x)N_(y) 2.00605 32 coating SiO₂1.48114 12 Scratch- AlO_(x)N_(y) 2.00605 2000 Resistant Layer 1 SiO₂1.48114 8.78 AlO_(x)N_(y) 2.00605 44.19 2 SiO₂ 1.48114 32.41AlO_(x)N_(y) 2.00605 24.3 3 SiO₂ 1.48114 58.55 AlO_(x)N_(y) 2.00605 7.47— — AS Glass 1.50542 Total coating thickness (nm) 2219.7

TABLE 16 Structure of Modeled Example 9. Refractive Physical Coating/Periods, if Index (at Thickness Layer applicable Material 550 nm) (nm)Ambient — Air 1 medium Optical 1 AlO_(x)N_(y) 2.00605 25 coating SiO₂1.48114 25 Scratch- AlO_(x)N_(y) 2.00605 2000 Resistant Layer 1 SiO₂1.48114 8.78 AlO_(x)N_(y) 2.00605 44.19 2 SiO₂ 1.48114 32.41AlO_(x)N_(y) 2.00605 24.3 3 SiO₂ 1.48114 58.55 AlO_(x)N_(y) 2.00605 7.47— — AS Glass 1.50542 Total coating thickness (nm) 2225.7

TABLE 17 Structure of Modeled Example 10. Refractive Physical Coating/Periods, if Index (at Thickness Layer applicable Material 550 nm) (nm)Ambient — Air 1 medium Optical SiO₂ 1.48114 2 coating 1 AlO_(x)N_(y)2.00605 25 SiO₂ 1.48114 25 Scratch- AlO_(x)N_(y) 2.00605 2000 ResistantLayer 1 SiO₂ 1.48114 8.78 AlO_(x)N_(y) 2.00605 44.19 2 SiO₂ 1.4811432.41 AlO_(x)N_(y) 2.00605 24.3 3 SiO₂ 1.48114 58.55 AlO_(x)N_(y)2.00605 7.47 — — AS Glass 1.50542 Total coating thickness (nm) 2227.7

TABLE 18 Structure of Modeled Example 11. Periods, Refractive PhysicalCoating/ if Index (at Thickness Layer applicable Material 550 nm) (nm)Ambient — Air 1 medium Optical SiO₂ 1.48114 100 coating 1 AlO_(x)N_(y)2.00605 34 SiO₂ 1.48114 15 Scratch- AlO_(x)N_(y) 2.00605 2000 ResistantLayer 1 SiO₂ 1.48114 8.78 AlO_(x)N_(y) 2.00605 44.19 2 SiO₂ 1.4811432.41 AlO_(x)N_(y) 2.00605 24.3 3 SiO₂ 1.48114 58.55 AlO_(x)N_(y)2.00605 7.47 — — AS Glass 1.50542 Total coating thickness (nm) 2324.7

FIGS. 13-14 show the calculated reflectance spectra and the calculatedreflected color, respectively, for only the anti-reflective surface ofModeled Example 8. FIGS. 15-16 show the calculated reflectance spectraand the calculated reflected color, respectively, for only theanti-reflective surface of Modeled Example 9. FIGS. 17-18 show thecalculated reflectance spectra and the calculated reflected color,respectively, for only the anti-reflective surface of Modeled Example10.

The optical performance of Modeled Examples 8-11 is summarized in Table22.

TABLE 22 Optical performance of Modeled Examples 8-11. Maximum AmountThickness Amount angular of low- of top- of Anti- color shift, indexmost high- reflective viewing material (user index surface angles onair- side) material reflectance, 0-60 side low in photopic degrees, ofindex top average D65 or thickest (e.g. 500 (%) F2, sample high- SiO₂)nm of Modeled (single referenced to index hard layer coated Exampleside) itself layer (nm) (nm) article (%) 8 7.85 1.1 12 0 97.6 9 4.9 2.725 0 95.0 10 4.9 3.0 27 2 94.6 11 1.3 2.2 115 100 77.0

As shown in FIGS. 13, 15, 17, and 19, Modeled Examples 8-11 exhibit lowreflectance (i.e., values less than about 10% and less than about 8%),for viewing angles of 8°, 20°, and 40°, with the reflectance for aviewing angle of 60° being slightly higher, over the optical wavelengthregime. Modeled Example 11 exhibited very low reflectance for viewingangles of 8°, 20°, 40° and 60° (e.g., a maximum average reflectance ofabout 7% or less). At viewing angles of 8°, 20°, and 40°, the averagereflectance is even lower (i.e., less than about 2%).

As shown in FIGS. 14 and 20, Modeled Examples 8 and 11 exhibited areflected color, at viewing angles from normal incidence to 60°, of lessthan about 2 for both D65 and F2 illuminants. As shown in FIGS. 16 and18, Modeled Example 9 and 10 exhibited a range of reflected color, atviewing angles from normal incidence to 60°, of less than about 3 forboth D65 and F2 illuminants.

It is believed that Examples 8-11 also exhibit the hardness valuesdescribed herein, as measured by the Berkovich Indenter Hardness Test(and, in particular, a hardness in the range from about 14 GPa to about21 GPa).

The optical performance of Modeled Examples 8-11 was compared to ModeledComparative Example 4. The optical performance evaluated includesaverage reflectance over the wavelength range from about 450 nm to about650 nm and color shift (with reference to a* and b* coordinates (−1,−1), using the equation √((a*_(example)−(−1))²+(b*_(example)−(−1))²))when viewed at an incident illumination angles in the range from about 0degrees to about 60 degrees from normal incidence under F02 and D65illuminants. Modeled Comparative Example 4 exhibited a lower averagereflectance, but also exhibited a significantly greater color shiftalong viewing angles from 0 degrees to 60 degrees.

Example 12

Example 12 included a 16-layer optical coating as shown in Table 23,including layers sequentially disposed on top of one another, anddisposed on a strengthened aluminosilicate glass substrate having anominal composition of about 65 mol % SiO₂, 5 mol % B₂O₃, 14 mol %Al₂O₃, 14 mol % Na₂O, and 2.5 mol % MgO.

TABLE 23 Structure of Example 12. Refractive Physical Layer MaterialIndex Thickness (nm) Medium Air 1 16 SiO₂ 1.4952 92.4 15Si_(u)Al_(v)O_(x)N_(y) 2.08734 150.1 14 SiO₂ 1.4952 10.1 13Si_(u)Al_(v)O_(x)N_(y) 2.08734 96.9 12 SiO₂ 1.4952 18.9 11Si_(u)Al_(v)O_(x)N_(y) 2.08734 41.9 10 SiO₂ 1.4952 40.1 9Si_(u)Al_(v)O_(x)N_(y) 2.08734 37.6 8 SiO₂ 1.4952 17.4 7Si_(u)Al_(v)O_(x)N_(y) 2.08734 2000.0 6 SiO₂ 1.4952 8.7 5Si_(u)Al_(v)O_(x)N_(y) 2.08734 41.0 4 SiO₂ 1.4952 29.9 3Si_(u)Al_(v)O_(x)N_(y) 2.08734 23.3 2 SiO₂ 1.4952 53.6 1Si_(u)Al_(v)O_(x)N_(y) 2.08734 7.2 Substrate Glass 1.50996 Total 2661.9Thickness

Both SiO₂ and Si_(u)Al_(v)O_(x)N_(y) layers were made by reactivesputtering in an AJA-Industries Sputter Deposition Tool. SiO₂ wasdeposited by DC reactive sputtering from an Si target with ion assist;Si_(u)Al_(v)O_(x)N_(y) material was deposited by DC reactive sputteringcombined with RF superimposed DC sputtering with ion assist. The targetswere 3″ diameter Silicon and 3″ diameter Al. The reactive gasses werenitrogen and oxygen, and the “working” (or inert) gas was Argon. Thepower supplied to the Silicon was radio frequency (RF) at 13.56 Mhz. Thepower supplied to the Aluminum was DC.

The sputtering process conditions used to form the optical coating ofExample 12 are shown in Table 23.

TABLE 24 Sputtering Process Conditions for Example 12. Al DC Al RF Si RFAr flow N₂ flow O₂ flow substrate Material power (W) power (W) power (W)(sccm) (sccm) (sccm) T (C) Si_(u)A_(v)lO_(x)N_(y) 300 200 500 30 30 0.5200 SiO₂ 50 (shutter 50 (shutter 500 30 30 3 200 closed) closed)

Example 13 exhibited the optical properties shown in Table 22 and Table23. Table 22 shows the reflected and transmitted color was measured fromboth the anti-reflective surface and the opposite, bare surface of thesubstrate (using a total reflectance or 2-sided measurement). Table 23shows the reflected color as measured from only the anti-reflectivesurface (using a single-sided measurement).

TABLE 25 Optical performance of Example 12, as measured on theanti-reflective surface and including the opposite, bare surface of thesubstrate. Reflectance color Transmittance color Illuminant D65 CIE x0.2874 CIE x 0.3163 y 0.3227 y 0.3323 L* 30.00 L* 97.26 a* −4.10 a* 0.61b* −3.19 b* 0.96 X 5.55 X 88.59 Y 6.23 Y 93.09 Z 7.53 Z 98.43 IllumiantA CIE x 0.4235 CIE x 0.4534 y 0.4082 y 0.4061 L* 29.27 L* 97.40 a* −4.43a* 0.76 b* −4.22 b* 1.12 X 6.17 X 104.33 Y 5.95 Y 93.43 Z 2.45 Z 32.33Illumiannt F2 CIE x 0.3567 CIE x 0.3820 y 0.3623 y 0.3690 L* 29.34 L*97.38 a* −3.05 a* 0.45 b* −3.29 b* 1.02 X 5.88 X 96.67 Y 5.97 Y 93.39 Z4.63 Z 63.00

TABLE 26 Optical performance of Example 12, as measured on theanti-reflective surface only. 1st surface reflectance 6° 20° 40° 60°Illuminant s + p pol s + p pol s + p pol s + p pol avg avg avg avg D65CIE x 0.2422 0.2383 0.2356 0.2732 y 0.3095 0.3047 0.2694 0.2944 L* 17.1215.88 13.99 25.12 a* −8.84 −8.55 −3.43 −1.27 b* −6.00 −6.48 −10.16 −7.81X 1.82 1.62 1.51 4.13 Y 2.33 2.08 1.73 4.45 Z 3.37 3.11 3.18 6.54 A CIEx 0.3640 0.3610 0.3608 0.4067 y 0.4136 0.4058 0.3765 0.3953 L* 15.5914.34 12.65 24.36 a* −10.20 −9.35 −5.95 −4.42 b* −8.26 −9.27 −12.66−8.67 X 1.78 1.59 1.44 4.33 Y 2.02 1.79 1.51 4.21 Z 1.09 1.03 1.05 2.11F2 CIE x 0.3111 0.3071 0.3038 0.3390 y 0.3523 0.3412 0.3045 0.3362 L*15.73 14.37 13.00 24.88 a* −6.94 −5.85 −1.41 −1.37 b* −6.41 −7.63 −11.68−8.55 X 1.81 1.61 1.56 4.41 Y 2.05 1.79 1.56 4.38 Z 1.96 1.85 2.01 4.23

Example 12 exhibited the hardness and Young's modulus, as measured onthe anti-reflective surface, as shown in Table 28. Both values weremeasured using a Berkovich indenter as described herein.

TABLE 27 Measured hardness and Young's modulus for Example 12. Modulus,GPa Hardness, GPa Example 12 169 17.6 Example 4 65 6.8

It will be apparent to those skilled in the art that variousmodifications and variations can be made without departing from thespirit or scope of the invention.

What is claimed is:
 1. An article comprising: a substrate having a majorsurface; and an optical coating disposed on the major surface andforming an anti-reflective surface, the optical coating comprising ananti-reflective coating, the article exhibiting a maximum hardness ofabout 12 GPa or greater as measured on the anti-reflective surface by aBerkovich Indenter Hardness Test along an indentation depth of about 100nm or greater; wherein the article exhibits a single side average lightreflectance measured at the anti-reflective surface of about 8% or lessover an optical wavelength regime in the range from about 400 nm toabout 800 nm and either one or both of: article transmittance colorcoordinates in the (L*, a*, b*) colorimetry system at normal incidenceunder an International Commission on Illumination illuminant exhibitinga reference point color shift of less than about 2 from a referencepoint as measured at the anti-reflective surface, the reference pointcomprising at least one of the color coordinates (a*=0, b*=0) and thetransmittance color coordinates of the substrate, and articlereflectance color coordinates in the (L*, a*, b*) colorimetry system atnormal incidence under an International Commission on Illuminationilluminant exhibiting a reference point color shift of less than about 5from a reference point as measured at the anti-reflective surface, thereference point comprising at least one of the color coordinates (a*=0,b*=0), the color coordinates (a*=−2, b*=−2), and the reflectance colorcoordinates of the substrate, wherein, when the reference point is thecolor coordinates (a*=0, b*=0), the color shift is defined by√((a*_(article))²+(b*_(article))²), wherein, when the reference point isthe color coordinates (a*=−2, b*=−2), the color shift is defined by√((a*_(article)+2)²+(b*_(article)+2)²), and wherein, when the referencepoint is the color coordinates of the substrate, the color shift isdefined by√((a*_(article)−a*_(substrate))²+(b*_(article)−b*_(substrate))²).
 2. Thearticle of claim 1, wherein the article exhibits an angular color shiftof about 5 or less at an incident illumination angle that is 20 degreesor greater, referenced to normal incidence, under an InternationalCommission on Illumination illuminant selected from the group consistingof A series illuminants, B series illuminants, C series illuminants, Dseries illuminants, and F series illuminants, wherein angular colorshift is calculated using the equation √((a*₂−a*₁)²+(b*₂−b*₁)²), witha*₁, and b*₁ representing the coordinates of the article when viewed atnormal incidence and a*₂, and b*₂ representing the coordinates of thearticle when viewed at the incident illumination angle.
 3. The articleof claim 2, wherein the article exhibits an angular color shift of about5 or less at all incident illumination angles in the range from about 20degrees to about 60 degrees.
 4. The article of claim 2, wherein thesubstrate has a hardness less than the maximum hardness of the article.5. The article of claim 1, wherein the article exhibits an abrasionresistance after a 500-cycle abrasion using a Taber Test on theanti-reflective surface comprising any one or more of about 1% haze orless, as measured using a hazemeter having an aperture, wherein theaperture has a diameter of about 8 mm, an average roughness Ra, asmeasured by atomic force microscopy, of about 12 nm or less, a scatteredlight intensity of about 0.05 (in units of 1/steradian) or less, at apolar scattering angle of about 40 degrees or less, as measured atnormal incidence in transmission using an imaging sphere for scattermeasurements, with a 2 mm aperture at 600 nm wavelength, and a scatteredlight intensity of about 0.1 (in units of 1/steradian) or less, at apolar scattering angle of about 20 degrees or less, as measured atnormal incidence in transmission using an imaging sphere for scattermeasurements, with a 2 mm aperture at 600 nm wavelength.
 6. The articleof claim 1, wherein the anti-reflective coating comprises a plurality oflayers, wherein the plurality of layers comprises a first low RI layer,a second high RI layer, and an optional third layer.
 7. The article ofclaim 6, wherein the anti-reflective coating comprises a plurality ofperiods such that the first low RI layer and the second high RI layeralternate.
 8. The article of claim 7, wherein the anti-reflectivecoating comprises up to about 10 periods.
 9. The article of claim 1,wherein the single side average light reflectance is about 2% or lessover the optical wavelength regime at a viewing angle in the range fromabout 6 degrees to about 40 degrees.
 10. The article of claim 1, whereinthe substrate comprises an amorphous substrate or a crystallinesubstrate.
 11. The article of claim 10, wherein the amorphous substratecomprises a glass selected from the group consisting of soda lime glass,alkali aluminosilicate glass, alkali containing borosilicate glass andalkali aluminoborosilicate glass.
 12. The article of claim 11, whereinthe glass is chemically strengthened and comprises a compressive stress(CS) layer with a surface CS of at least 250 MPa extending within thechemically strengthened glass from a surface of the chemicallystrengthened glass to a depth of layer (DOL) of at least about 10 μm.13. The article of claim 1, further comprising an easy-to-clean coating,a diamond-like coating or a scratch-resistant coating disposed on theoptical coating.
 14. The article of claim 1, wherein the optical coatingcomprises a scratch resistant layer having a thickness in the range fromabout 1 micrometer to about 3 micrometers.
 15. The article of claim 14,wherein the anti-reflective coating is disposed between scratchresistant layer and the substrate.
 16. The article of claim 14, whereinthe scratch resistant layer is disposed between the substrate and theanti-reflective coating.
 17. The article of claim 14, wherein theanti-reflective coating comprises a first portion and a second portion,and wherein the scratch resistant layer is disposed between the firstportion and the second portion.
 18. An article comprising: a substratehaving a major surface; and an optical coating disposed on the majorsurface forming an anti-reflective surface, wherein the optical coatingcomprises at least one anti-reflective coating and a scratch resistantlayer disposed between the anti-reflective coating and the substrate,wherein the article exhibits a maximum hardness of about 12 GPa orgreater as measured on the anti-reflective surface by a BerkovichIndenter Hardness Test along an indentation depth of about 50 nm orgreater, wherein the article exhibits, under a D65 or F2 illuminant atnormal incidence, an average visible photopic reflectance of about 10%or less over the optical wavelength regime, as measured on theanti-reflective surface. article transmittance color coordinates in the(L*, a*, b*) colorimetry system exhibiting a reference point color shiftof less than about 2 from a reference point as measured at theanti-reflective surface, the reference point comprising at least one ofthe color coordinates (a*=0, b*=0) and the transmittance colorcoordinates of the substrate, and article reflectance color coordinatesin the (L*, a*, b*) colorimetry system exhibiting a reference pointcolor shift of less than about 5 from a reference point as measured atthe anti-reflective surface, the reference point comprising at least oneof the color coordinates (a*=0, b*=0), the color coordinates (a*=−2,b*=−2), and the reflectance color coordinates of the substrate, wherein,when the reference point is the color coordinates (a*=0, b*=0), thecolor shift is defined by √((a*_(article))²+(b*_(article))²), wherein,when the reference point is the color coordinates (a*=−2, b*=−2), thecolor shift is defined by √((a*_(article)+2)²+(b*_(article)+2)²), andwherein, when the reference point is the color coordinates of thesubstrate, the color shift is defined by√((a*_(article)−a*_(substrate))²+(b*_(article)−b*_(substrate))²). 19.The article of claim 18, wherein the article exhibits an angular colorshift of about 5 or less at an incident illumination angle that is 20degrees or greater from normal incidence, under an InternationalCommission on Illumination illuminant selected from the group consistingof A series illuminants, B series illuminants, C series illuminants, Dseries illuminants, and F series illuminants, wherein angular colorshift is calculated using the equation √((a*₂−a*₁)²+(b*₂−b*₁)²), witha*₁, and b*₁ representing the coordinates of the article when viewed atnormal incidence and a*₂, and b*₂ representing the coordinates of thearticle when viewed at the incident illumination angle.
 20. The articleof claim 18, wherein the substrate has a hardness less than the maximumhardness of the article.
 21. The article of claim 18, wherein theanti-reflective coating comprises a plurality of layers, the pluralityof layers comprising at least one first low RI layer and a second highRI layer, and the combined thickness of the first low RI layers or thecombined thickness of the second high RI layers is less than about 500nm.
 22. The article of claim 18, wherein the average visible photopicreflectance is about 2% or less over the optical wavelength regime. 23.The article of claim 18, wherein the substrate comprises an amorphoussubstrate or a crystalline substrate.
 24. The article of claim 18,wherein the optical coating comprises a thickness and a plurality oflayers comprising a nitride or oxy-nitride material, and where thecombined thickness of the layers comprising a nitride or an oxyinitrideis 50% or greater of the thickness of the optical coating.
 25. Thearticle of claim 18, wherein the scratch-resistant layer comprises anitride or an oxy-nitride material and has a thickness of 200 nm orgreater, and wherein the anti-reflective coating comprises a pluralityof high refractive index layers having a refractive index greater thanabout 1.85 and a plurality of low refractive index layers having arefractive index less than about 1.75.
 26. The article of claim 18,wherein the plurality of high refractive index layers comprises anitride or oxy-nitride material, and the plurality of low refractiveindex layers have a combined thickness of less than about 200 nm. 27.The article of claim 18, wherein the angular color shift is less thanabout
 2. 28. The article of claim 18, wherein the optical coatingcomprises a thickness and a plurality of layers comprising a highrefractive index material with a refractive index greater than about1.8, and wherein the combined thickness of the plurality of layerscomprising the high refractive index material is 50% or greater of thethickness of the optical coating.
 29. The article of claim 18, whereinthe optical coating comprises a thickness and a plurality of layerscomprising a high refractive index material with a refractive indexgreater than about 1.8, and wherein the combined thickness of theplurality of layers comprising a high refractive index material is 70%or greater of the top-most 500 nm of the optical coating.
 30. Thearticle of claim 18, wherein the substrate has a hardness less than themaximum hardness of the article.